[MCQ's]Engineering Mechanics - Last Moment Tuitions

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[MCQ’s]Engineering Mechanics

System of Coplanar Forces

1. In right-handed coordinate system which axis is considered to be positive?
a) The thumb is z-axis, fingers curled from x-axis to y-axis
b) The thumb is x-axis, fingers curled from z-axis to y-axis
c) The thumb is y-axis, fingers curled from x-axis to z-axis
d) The thumb is z-axis, fingers curled from y-axis to x-axis

Answer: a
Explanation: As right-handed coordinate system means that you are curling your fingers from positive x-axis towards y-axis and the thumb which is projected is pointed to the positive z-axis. Thus visualizing the same and knowing the basic members of the axis will not create many problems.

2. If A is any vector with Ai + Bj + Ck then what is the y-axis component of the vector?
a) B units
b) A units
c) C units
d) Square root of a sum of squares of the three, i.e. A, B and C

Answer: a
Explanation: As the given vector is shown in the Cartesian system, the number with “j” is the Y-axis component of the given vector. With the numbers with “i” representing components of x-axis and “k” representing the z axis respectively.

3. If the force vector F is having its x-axis component being equal to Z N, y-axis component be X N and z-axis component be Y N then vector F is best represented by?
a) Xi + Yj + Zk
b) Yi + Xj + Zk
c) Zi + Yj + Xk
d) Zi + Xj + Yk

Answer: d
Explanation: It is given that x, y and z-axis components are Z, X and Y respectively. Thus, just by placing the right coordinates we get option d to be correct. Here just the interchange of the axis’s representor with their respective axis is creating confusion. Which must be figured out.

4. Which statement is right for force vector F = Ai + Bj + Ck?
a) In rectangular components representation of any vector we have vector F = Ai + Bj + Ck
b) In rectangular components representation of any vector we have vector F = Ax + By + Cz
c) In rectangular components representation of any vector we have vector F = Fx + Fy + Fz
d) In rectangular components representation of any vector we have vector F = Fi + Fj + Fk

Answer: c
Explanation: As given the vector is F = Ai + Bj + Ck, this implies that the x ,y and z-axis components of this vector is A, B and C respectively. But, in rectangular components representation of any vector, the vector is written as F = Fx + Fy + Fz.

5. What is the magnitude of the Cartesian vector having the x, y and z axis components to be A, B and C?
a) Square root of the squares each A, B and C
b) Square of the squares each A, B and C
c) Cube root of the squares each A, B and C
d) Cube of the squares each A, B and C

Answer: a
Explanation: The magnitude of a Cartesian vector having the x, y and z axis components to be A, B and C is always the square root of the squares each A, B and C. This comes from the distance formula between two points in the Cartesian plane. That is the square root of the subtraction of the final and initial point of a line.

6. What is cosα for force vector F = Ax + By +Cz (Given α, β and γ are the angles made by the vector with x, y and z axis respectively)?
a) B/F
b) C/F
c) A/F
d) 1

Answer: c
Explanation: The cosine component of the vector is defined as the ratio of the x-axis component to the magnitude of the vector, i.e. F in this case. Likewise, the sine component is the ratio of the y-axis component to the magnitude of the vector.

7. What is the sum of squares of the cosine angles made by the force vector with the coordinate axis?
a) 1
b) ½
c) 2
d) 3

Answer: a
Explanation: The sum of the squares of the cosines of the vector will give you the squares of the components in the numerator, and the vector’s magnitude’s square in the denominator. But the numerator sum is equal to the vector’s magnitude’s square. Thus, the answer = 1.

8. What is the x-axis component of the force vector Ai + Bj +Ck with magnitude equal to F?
a) B
b) C
c) Fcosα
d) Fcosβ

Answer: c
Explanation: As we know that the cosα is the ratio of the x-axis component to the magnitude of the vector. Thus the x-axis components is Fcosα, F, the magnitude in the case. Likely if we want to take the y-axis component we would try to do the same with the sine component.

9. We can add the force vectors directly. But with dividing each by it’s magnitude first.
a) True
b) False

Answer: b
Explanation: False, because if you will divide the magnitude of the vector to itself than the resulting would be the unit vector. Which is just giving you the direction of the vector, not the vector itself. This means unit vector has direction same as it’s respective vector but having a magnitude equal to one.

10. For a vector F, Fcosβ is equal to zero. What does this refer?
a) X-axis component is zero
b) Y-axis component is zero
c) Z-axis component is zero
d) β = 180˚

Answer: b
Explanation: As we know the α, β and γ are the angles made by the x, y and z-axis respectively. Thus y-axis component is zero, or β = 90˚. And thus if the angle is giving component to be zero this means the vector in that particular axis is perpendicular to that axis.

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11. Which statement is correct about the vector F?
a) F= Fcos β + Fcos α + Fcosγ
b) F= Fsin β + Fcos α + Fcosγ
c) F= Fcos β + Fsin α + Fcosγ
d) F= Fcos β + Fcos α + Fsinγ

Answer: a
Explanation: As we know the α, β and γ are the angles made by the x, y and z-axis respectively. Thus, is the magnitude of the vector is F, the F= Fcos β + Fcos α + Fcosγ. Which means the force is the resultant of all its axis’ components.

12. Which is true?
a) ∑F = ∑Fx + ∑Fy + ∑Fz
b) ∑F = -(∑Fx + ∑Fy + ∑Fz)
c) ∑F = ∑Fxi + ∑Fyj + ∑Fzk
d) ∑F = -(∑Fxi+ ∑Fyj + ∑Fzk)

Answer: c
Explanation: The total of two or more forces is equal to the sum of their respective axis’s components. That is the resultant adds up all the components of the forces in their respective axis, whether it may be x, y or z axis.

13. Find the angle α, for the vector making an angle by y and z axis as 60˚ and 45˚ respectively. It makes an angle of α with x-axis. The magnitude of the force is 200N.
a) 60˚
b) 120˚
c) 45˚
d) 90˚

Answer: a
Explanation: When you will resolve the vector in its x, y and z-axis components, you will get an equation containing cosα. After getting the α correctly, you need to directly put that value in the previous equation of components. α = 60˚. As 120˚ will give a negative component. Just try to resolve the vector in its components.

16. For two vectors A and B, what is A.B (if they have angle α between them)?
a) |A||B| cosα
b) |A||B|
c) √(|A||B|) cosα
d) |A||B| sinα
Answer: a
Explanation: The dot product of the two vectors is always the product of the magnitudes of the two forces and the cosine of the angle between them. We need to consider the triangle and then accordingly apply the trigonometry. This is one of the ways of resolving the components.

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17. Which statement is right?
a) Communitive law: A.B =B.A
b) Multiplicative law: a(A.B) = Ax(aB)
c) Multiplicative law: A.(B+D) = (A.B) + (A.D)
d) Communitive law: a(A.B) = A.(aB)

Answer: a
Explanation: For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).

18. What is Distributive law?
a) A.B =B.A
b) a(A.B) = A.(aB)
c) A.(B+D) = (A.B) + (A.D)
d) a(A.B) = AxB

Answer: c
Explanation: For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).

19. What is multiplication law?
a) A.B =B.A
b) a(A.B) = A.(aB)
c) A.(B+D) = (A.B) + (A.D)
d) a(A.B) = AxB

Answer: b
Explanation: For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).

20. Which is true for two vector A = A1i + A2j + A3k and B = B1i + B2j + B3k?
a) A.B = A1B1 + A2B2 + A3B3
b) AxB = A1B1 + A2B2 + A3B3
c) A.B = A1B2 + A2B3 + A3B1
d) AxB = A1B2 + A2B3 + A3B1

Answer: a
Explanation: The multiplication of x, y and z components with their respective same component gives a scalar, equal to 1, i.e. i.i = 1 and j.j = 1, while jxj =0. This is the basic principle of vector algebra which needs to apply wherever needed.

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22. What is k.i?
a) 0
b) 1
c) -1
d) ∞

Answer: a
Explanation: As the dot product of only the same Cartesian component is unity, i.e. i.i = 1 and j.j =1, rest all remaining dot product will give 0(i.j = 0 and j.k = 0). Cross product of the same plane vectors always gives zero. And dot product of the same plane vector gives a scalar quantity.

23. What is {(i.i) + (-i.j) + (-k.k) + (k.i)}.(Ai +Bj + Cz)?
a) 1
b) 0
c) A + B + C
d) -1

Answer: b
Explanation: {(i.i) + (-i.j) + (-k.k) + (k.i)} = 0. As (1 + 0 + 0 – 1). Cross product of the same plane vectors always give zero. And dot product of the same plane vector gives a scalar quantity.

24. α = cos-1(A.B/AB). What is the range of α?
a) 0˚<α<90˚
b) 0˚<α<180˚
c) 90˚<α<180C
d) 0˚<α<45˚

Answer: b
Explanation: Cosine inverse function is defined only between 0˚ to 180˚. It cannot be defined under any of the given ranges, because this is the principal range of the inverse cosine function.

25. What is the value of {(AxB).(C.D)x(AxB).(C.D)}? For the four vectors A, B, C and D, with A, B, C and D all lying in the same plane?
a) i + j + k
b) √3(i + j + k)
c) 0
d) -1(i + j + k)

Answer: c
Explanation: Here we are trying to do the cross product of the two vectors in the same plane. Which will give us zero. While dot product of the same plane vector will give a scalar quantity, not zero.

26. What is (AxB).(BxA); or A = A1i + A2j + A3k and B = B1i + B2j + B3k?
a) 0
b) A1B1A2B2i + A2B2A3B3j + A3B3A1B1k
c) A1B1A1B2i + A2B2A3B2j + A3B3A1B3k
d) A1B1A2B1i + A2B2A2B3j + A3B3A2B1k

Answer: a
Explanation: Here we are trying to do the cross product of the two vectors in the same plane. Which will give us zero. While dot product of the same plane vector will give a scalar quantity, not zero.

30. Which of the following statement is true?
a) A scalar is any physical quantity that can be completely specified by its magnitude
b) A vector is any positive or negative physical quantity that can be completely specified by its magnitude
c) A scalar is any physical quantity that requires both a magnitude and a direction for its complete description
d) A scalar is any physical quantity that can be completely specified by its direction

Answer: a
Explanation: A scalar is any positive or negative physical quantity that can be completely specified by its magnitude. Examples of scalar quantities include length, mass, time, etc.

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31. For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents:
a) Their magnitude’s square and direction of the line of action respectively
b) Their magnitude and direction of the line of action respectively
c) Magnitude’s square root and direction of the line of action respectively
d) Magnitude’s square and the ratio of their lengths respectively

Answer: b
Explanation: For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents the magnitude and direction of the line of action respectively. The head/tip of the arrow indicates the sense of direction of the vector.

32. If a vector is multiplied by a scalar:
a) Then its magnitude is increased by the square root of that scalar’s magnitude
b) Then its magnitude is increased by the square of that scalar’s magnitude
c) Then its magnitude is increased by the amount of that scalar’s magnitude
d) You cannot multiply the vector with a scalar

Answer: c
Explanation: If a vector is multiplied by a scalar then its magnitude is increased by the amount of that scalar’s magnitude. When multiplied by a negative scalar it going to change the directional sense of the vector.

33. All the vectors quantities obey:
a) Parallelogram law of addition
b) Parallelogram law of multiplication
c) Parallelogram law of addition of square root of their magnitudes
d) Parallelogram law of addition of square of their magnitudes

Answer: a
Explanation: All the vectors quantities obey the parallelogram law of addition. Two vectors A and B (can be called as component vectors) are added to form a resultant vector. R = A+B.

34. A force vector with magnitude R and making an angle α with the x-axis is having its component along the x-axis and y-axis as:
a) Rcosine (α) and Rsine(α)
b) Rcosine (180-α) and Rsine(α)
c) Rcosine (180-α) and Rsine(180+α)
d) Rcosine (α) and Rsine(180+α)

Answer: a
Explanation: The component along the x-axis is the cosine component of the vector. And the y-axis component of the vector is the sine component if the angle is being made with the x-axis. And 180- α for some of the trigonometric function may change their sign.

35. Dividing the X-axis component and the Y-axis component of the vector making an angle with Y-axis α will give us.
a) Cot α
b) Tan α
c) Sec α
d) 1

Answer: b
Explanation: As the X-axis component of the vector becomes cos(90- α) and the Y-axis component becomes sin(90- α).Thus the division of both will give us Tan α.

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38. The magnitude of the resultant of the two vectors is always_____________
a) Greater than one of the vector’s magnitude
b) Smaller than one of the vector’s magnitude
c) Depends on the angle between them
d) Axis we choose to calculate the magnitude

Answer: c
Explanation: Yes, the magnitude of the resultant of the two vectors always depends on the angle between them. It might be greater or smaller than one of the vector’s lengths. For perfectly saying, it does depend upon the angle between them.

39. If two equal vector forces are mutually perpendicular then the resultant force is acting at which angle as compared to one of the vectors?
a) 45 degree
b) 90 degree
c) 180 degree
d) 0 degree

Answer: a
Explanation: The vectors are mutually perpendicular, this means that the angle between the forces is 90 degrees. Thus the results will form at 45 degrees to any of the vectors.

40. What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at the origin as, one being parallel to and heading towards positive x-axis and the other making 165 degrees with it and heading in the opposite direction of that of the first one?
a) It is either in the 1st quadrant or in the 2nd quadrant
b) It is either in the 1st quadrant or in the 3rd quadrant
c) It is either in the 1st quadrant or in the 4th quadrant
d) Only in the 1st quadrant

Answer: c
Explanation: If one is heading towards positive X-axis and the other is in the other direction opposite to the first one, with both having the same length and having an angle between them being obtuse, means that the direction is to be in the direction of either 1st quadrant or in the 4th quadrant.

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41. Force vector R is having a______________
a) Length of R and a specific direction
b) Length of R
c) A specific direction
d) Length of magnitude equal to the square root of R and a specific direction

Answer: a
Explanation: As it is a force vector, it means it is going to have a direction and a magnitude. The magnitude is not the square root of R, R is just the magnitude of the vector given.

42. The resultant of three equal vectors having mutual angles being 120 degrees and being originated from a single point is zero.
a) True
b) False

Answer: a
Explanation: As one can imagine three vectors coming out of a single point and are having a 120-degree angle with their adjacent ones, the resultant would be zero.

43. Every point on the force vector is having the same magnitude and the same direction as the whole force vector have.
a) True
b) False

Answer: b
Explanation: The vector is made by joining the final and the starting point. If we consider any arbitrary point then the length would be calculated w.r.t the starting point, which might give different magnitude but same direction.

45. What does the moment of the force measure?
a) The tendency of rotation of the body along any axis
b) The moment of inertia of the body about any axis
c) The couple moment produced by the single force acting on the body
d) The total work is done on the body by the force

Answer: a
Explanation: The moment of the force measures the tendency of the rotation of the body along any axis, whether it be the centroid axis of the body or any of the outside axis. The couple moment is produced by two forces, not by a single force. The total work done is the dot product of force and distance not the cross.

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46. If a car is moving forward, what is the direction of the moment of the moment caused by the rotation of the tires?
a) It is heading inwards, i.e. the direction is towards inside of the car
b) It is heading outwards, i.e. the direction is towards outside of the car
c) It is heading forward, i.e. the direction is towards the forward direction of the motion of the car
d) It is heading backward, i.e. the direction is towards the back side of the motion of the car

Answer: a
Explanation: When you curl your wrist in the direction in which the tires are moving then you will find that the thumb is pointing outwards. That is outwards the body of the car. This phenomenon is also observed in rainy seasons. When cars travel on the roads, the water is thrown outside from the tires, due to moment.

47. The tendency of rotation of the body along any axis is also called ___________
a) Moment of inertia
b) Moment of couple
c) Torque
d) Force

Answer: c
Explanation: The tendency of rotation of the body along any axis also called the torque. It is the moment of the force acting perpendicular to the direction of the axis of rotation. If the axis and the force are meeting at any point then there is no moment applied by the force.

48. The moment of the force is the product of the force and the perpendicular distance of the axis and the point of action of the force.
a) True
b) False

Answer: a
Explanation: The moment is the product of the force applied to the body and the perpendicular distance of the point of action of the force to the axis about which the body is being rotated. That is the moment is the cross product of the force and the distance between the axis and the point of action.

50. The moment axis is in the direction perpendicular to the plane of the force and the distance.
a) True
b) False

Answer: a
Explanation: The moment axis is always perpendicular to the planes of the force and the distance of the axis and the point of action of the force on the body. This means that the moment is the cross product of the force and the distance between the axis and the point of action of the force.

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54. Couple is having a combination of two forces. They are different in magnitude.
a) True
b) False

Answer: b
Explanation: The couple is a combination of two forces of the same magnitude. They are acting in the same sense of rotation. That is they are acting in the opposite direction but giving the body a rotation in the same direction. Whether it may be in a clockwise direction or anti-clockwise.

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56. The distance between the forces acting in the couple is ____________
a) Infinity
b) Zero
c) A finite distance
d) A circular loop

Answer: c
Explanation: The distance between the forces acting in the couple is having a finite distance. Couple is the combination of two forces which are acting in the same sense of rotation. That is they are acting in the opposite direction to provide the same direction rotation.

57. The resultant force acting in the couple is _________
a) Zero
b) Infinite
c) Twice the magnitude of the single force
d) Half the magnitude of the single force

Answer: a
Explanation: The resultant of the force acting on the couple is always zero. As the force are acting in the opposite directions. So if we add the forces algebraically then the sum is going to be zero. Or in other words, they cancel each other.

58. A man is travelling in the car. He is driving the car. If he is taking a turn in the road. He is applying force to the steering wheel by holding the wheel with his both hands. The steering wheel is facing a moment of force.
a) True
b) False

Answer: b
Explanation: The man is trying to rotate the wheel by applying the force. The force is being applied on the steering wheel. Which is rotating the wheel, but it is the moment of the couple. Because the man has holded the wheel with his both hands, hence it is not the moment of the force.

59. Which of the following is correct for the moment of couple M caused by two forces of same magnitude F and are separated by a distance of r?
a) M = rxF
b) M = r.F
c) M = -(rxF)
d) M = -(r.F)

Answer: a
Explanation: The answer is M = rxF. The moment id the cross product of the distance and the forces. It is the direction as directed by the curling of the hand. The thumb representing the direction of the moment. And the motion of the finger, that is the rotation gives the direction of the rotation caused by the forces.

60. A couple moment is a _______ vector.
a) Gradient
b) Scalar
c) Del
d) Free

Answer: d
Explanation: A couple moment is a free vector. It can act anywhere between the forces. As the couple is formed by two forces acting in the opposite directions. These forces are separated by a distance r, say, then the moment caused by them can act anywhere in between these forces.

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62. Which of the following is correct?
a) The couple moment depends on the axis of rotation
b) The couple moment depends directly on the radius vector of forces
c) The couple moment depends only on the distance vector between the forces
d) The couple moment’s direction is given by the left hand rule

Answer: c
Explanation: The couple moment depends only on the distance vector between the forces. The radius vector of the forces are not making the couple depended over it. But the distance vector is driven by subtracting the radius vectors of the forces. This means that the moment of the couple doesn’t directly depend on the radius vector of forces.

63. If the forces acting on the couple are in the same direction, that is they are not in the opposite direction as always they are, then?
a) The direction of the forces doesn’t determine the moment
b) The couple moment will be maximum
c) The couple is not possible
d) No change occurs

Answer: c
Explanation: The forces are always in the opposite direction for the couple moment. But if they don’t act like the same, that is they change their directions and align themselves in the same direction then the couple is not possible.

65. The resultant couple moment is ____________ sum of various couples acting on the body.
a) Vector
b) Scalar
c) Scalar Triple
d) Dot

Answer: a
Explanation: As we know that the moment is vector quantity, their summation requires vector math. The couple moment is also the same. That is they are also the vectors and requires vector math. Thus the resultant couple moment is the vector sum of the various couples acting in the body.

67. If two forces magnitude F each are acting in the Cartesian coordinate and are acting at the points A(3,3) and B(-3,3). They are heading towards negative z direction and positive z direction respectively. The distance between them is given as r. The radius vectors of the force at A and B are Ra and Rb respectively. Then the moment is given as:
a) (Ra-Rb).F
b) (Rb-Ra).F
c) (Ra-Rb)xF
d) (Rb-Ra)xF

Answer: d
Explanation: The moment of a couple as we know is the cross product of the force and the distance between them. But in this case, we are given the radius vectors of the forces. So when we apply the vector maths to find the distance between the forces we get that the distance r = Rb-Ra. Now that we have the distance, we cross it with the force.

Equilibrium of System of Coplanar Force

1. What is not the condition for the equilibrium in three dimensional system of axis?
a) ∑Fx=0
b) ∑Fy=0
c) ∑Fz=0
d) ∑F≠0

Answer: d
Explanation: For the equilibrium in the three dimensional system of axis we have all the conditions true as, ∑Fx=0, ∑Fy=0 and ∑Fz=0. Also, we have the summation of the forces equal to zero. Which is not a non-zero value.

2. We first make equilibrium equations and then the free body diagram and then solve the question.
a) True
b) False

Answer: b
Explanation: We first make the free body diagram and then we make the equilibrium equations to satisfy the given conditions. This helps us to solve the question easily. As this reduces the part of imagination and increases accuracy too.

Answer: a
Explanation: As the system is in equilibrium so we need to balance the forces. So when applying the condition of net force to be zero in the z direction, we get (2/3)FAD = 600N. This gives us force along AD be 900N.

Answer: a
Explanation: The application of the equilibrium equation will yield the result. That is the resultant along the z-axis will remain zero. Which give the value of γ as 50˚. And therefore q=51.9cm.

7. ∑Fx=0, ∑Fy=0 and ∑Fz=0 are vector equations.
a) True
b) False

Answer: b
Explanation: The answer is false as the equations asked are scalars. As we make the net sum of the forces along the axis equal to zero. Of course this equation comes from the solving the vector forms, but still, the result is a scalar, hence the equations are scalar.

8. When the body is in equilibrium then which of the following is true?
a) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude
b) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude square
c) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude square root
d) We equate all the components of the forces acting on the body equal to zero

Answer: d
Explanation: Yes, we equate all the components of the three axis equal to zero. That is the resultant of the forces along the three axis are being equated to zero. This brings in that there is no net force in any direction. Hence equilibrium.

9. If solving the question in 3D calculations is difficult, then use the 2D system and then equate the total net force to zero.
a) True
b) False

Answer: a
Explanation: The answer is obviously yes. If we are having any difficulty in making the vector components, then we can go in 2D. As if the particle is in equilibrium, the net force will be zero. No matter where you see first. Net force is zero.

10. If the resolved force or the force which you get as the answer after solving the question is negative, then what does this implies?
a) The force is in the reverse direction w.r.t the direction set in the free body diagram
b) The force is not in the reverse direction w.r.t the direction set in the free body diagram
c) The force component is not possible
d) The force is possible, but in the direction perpendicular to the resultant force

Answer: a
Explanation: The negative sign implies things in the opposite manner. If the force is coming negative this doesn’t mean that it is impossible. But it means that the force is in the opposite direction w.r.t the direction set by you in the free body diagram.

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11. An electromagnet crane is carrying the electromagnet with the help of the three cables. But the electromagnet is not stable because of the wind. What is science behind the cause?
a) The wind is making the net force of the body equal to a non-zero value
b) The wind is making the net force of the body equal to zero value
c) The wind is making the net force of the body equal to a non-zero value but is supporting the equilibrium
d) The wind is making the net force of the body equal to zero value and supporting equilibrium

Answer: a
Explanation: Anybody is in equilibrium only if the net force along the three axis is zero. But in this case, the wind is not helping the body to do so. The science behind this is that the resultant forces are being equated to a non-zero value by the wind. Hence unstable.

12. If anybody is tied to three or more ropes, and then is allowed to achieve its equilibrium. Then the equilibrium achieved is achieved w.r.t what?
a) The three axis of the body
b) The ground
c) The ropes direction
d) The weight direction

Answer: b
Explanation: Yes, the equilibrium is being achieved w.r.t the ground. Like the motion, w.r.t ground need be zero. That is the relative velocity of the object or the body must be zero w.r.t the ground. This means motion is in equilibrium.

13. The main condition for the rigid body is that the distance between various particles of the body does change.
a) True
b) False

Answer: b
Explanation: The main condition for the rigid body is that the distance between various particles of the body does not change. If the distance does change the body is not to be called as rigid. Thus the fix distance of the particles is very much required for the equilibrium of the rigid body.

15. What does Newton’s third law states?
a) The rate of change of momentum is equal to the force applied
b) For every reaction, there is an opposite reaction
c) The body tends to be rotated if the force is applied tangentially
d) The body is rest until a force is applied

Answer: b
Explanation: The requirement of the third law is important in the equilibrium of the body. Especially the rigid bodies. The rigid body particles are in the equilibrium and are thus facing the forces and to be in the equilibrium they also react and apply the opposite force and thus the third law of Newton.

17. For equilibrium, the net force acting on the body is zero.
a) True
b) False

Answer: a
Explanation: The equilibrium is only attained if the net force on the body tends to be equal to zero. Thus the forces cancel out. If this happens there is no motion of the body along with any direction and hence the body is said to be in equilibrium. The body here is a rigid body.

18. For equilibrium, the net moment acting on the body by various forces is zero.
a) True
b) False

Answer: a
Explanation: The equilibrium is only attained if the net moment on the body tends to be equal to zero. Thus the moments caused by different forces cancel out. If this happens there is no motion of the body along with any direction and hence the body is said to be in equilibrium. The body here is a rigid body.

20. The net moment of the body is zero that means the distance between the force and the rotational axis is zero.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: c
Explanation: The net moment of the body is zero that doesn’t mean that the distance between the force and the rotational axis is zero. This means moments caused by different forces cancels out. If this happens there is no motion of the body along with any direction and hence the body is said to be in equilibrium.

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22. The net force of the body is zero that means the force are not being applied to the body at all and hence the body is in equilibrium.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: c
Explanation: The net force of the body is zero that doesn’t mean that the force are not being applied to the body at all and hence the body is in equilibrium. The equilibrium is only attained if the net force on the body tends to be equal to zero. Thus the forces cancels out. If this happens there is no motion of the body along any direction and hence the body is said to be in equilibrium.

23. Which of the following is correct?
a) The application of the conditions of the equilibrium of the body is valid only in the 2D
b) The application of the conditions of the equilibrium of the body is valid only in the 3D
c) The application of the conditions of the equilibrium of the body is valid only in the 1D
d) The application of the conditions of the equilibrium of the body is valid throughout

Answer: d
Explanation: The application of the conditions of the equilibrium of the body is valid throughout. This means that the conditions are irrespective of the dimensions. The conditions are the basic rules that define the equilibrium of the body and thus are applicable in any dimension of the real axis.

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25. To satisfy the conditions of the equilibrium, the must not only be having a net force zero, but also be properly held or constrained on its supports.
a) True
b) False

Answer: a
Explanation: To satisfy the conditions of the equilibrium, the must not only be having a net force zero, but also be properly held or constrained on its supports. The more the stable are the supports the more the stable is the equilibrium, that is the more easily is the equilibrium is achived.

Answer: a
Explanation: As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.

27. What is redundant support?
a) The supports consisting of hinge and a roller
b) The supports consisting of hinge only
c) The supports consisting of roller only
d) The supports more than necessary to hold the structure

Answer: d
Explanation: The supports if are more than the supports required to hold the structure are termed as the reductant supports. It becomes statically indeterminate. This not only creates a problem in achieving the equilibrium but also affects the calculation of the equilibrium.

29. Statically indeterminacy means?
a) There will be less equations available for equilibrium than the unknown loadings
b) There will be more equations available for equilibrium than the unknown loadings
c) There will be equal equations available for equilibrium as the unknown loadings
d) The support reactions are opposite to each other

Answer: a
Explanation: Statically indeterminacy is the condition when less equations are available for equilibrium than the unknown loadings. This not only creates a problem in achieving the equilibrium but also affects the calculation of the equilibrium. Thus this is the stuff which one needs to prevent from happening.

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31. The additional equations invented in the statically indeterminacy condition is solved by __________
a) Deformation conditions at the point of supports
b) Rotational equations
c) Translation equations
d) Linear rotation equations

Answer: a
Explanation: The additional equations invented in the statically indeterminacy condition is solved by deformation conditions at the point of supports. This are the conditions which are based on the physical and the chemical properties of the body. A different study for this is done in mechanics of material.

32. The generation of equal equations available for equilibrium as the unknown loadings always guarantees the stability of the body.
a) True
b) False

Answer: b
Explanation: The generation of equal equations available for equilibrium as the unknown loadings doesn’t always guarantees the stability of the body. It is defined on the basis of the supports that are their supporting the body. Or it also depends on the types of the forces that are acting, i.e. the three or two force system.

33. In 3D the body will be improperly constrained if the axis is intersected by the reaction forces.
a) The statement is right
b) The statement is wrong
c) The statement is right if there is ‘2D’
d) The statement is right if there is ‘support reaction’

Answer: a
Explanation: In 3D the body will be improperly constrained if the axis is intersected by the reaction forces. This is because there will be small moments which will occur in the real situations. But they will not be matched in the calculations done for determining the equilibrium. Thus the statement is right.

34. The improper constraining leading to instability occurs when ___________________
a) The reactive forces are parallel
b) The reactive forces are perpendicular
c) The reactive forces are equal
d) The reactive forces are rotationa

Answer: a
Explanation: If the forces are parallel (the reactive forces) then this creates an instability. That is this is also a type of improper constraining which is resulting in instability of the structure. Thus reactive forces are parallel are resulting in the instability of the body.

36. What is partially constrained?
a) There will be less equations available for equilibrium than the reactive forces
b) There will be more equations available for equilibrium than the reactive forces
c) There will be equal equations available for equilibrium as the reactive forces
d) The support reactions are opposite to each other

Answer: b
Explanation: The situation may arise when there will be more equations available for equilibrium than the reactive forces. This condition is known as partially constrained. This is also one of the factor which is giving instability to the structure.

37. If all the reactive forces are intersecting at the common point or pass through a common axis when _____________
a) The body is in equilibrium
b) The body is said to be achieve stability but no equilibrium
c) The body is said to be improperly constrained
d) The body is in deformation

Answer: c
Explanation: If all the reactive forces are intersecting at the common point or pass through a common axis then the body is said to be improperly constrained. Whether it may be the reactive forces being parallel. Or be it the forces meeting at a common point. The body is said to be improperly constrained.

39. A force is developed by a support that not allows the ________ of its attached member.
a) Translation
b) Rotation
c) Addition
d) Subtraction

Answer: a
Explanation: The force developed by a support doesn’t allow the translation of its attached member. This is the basic condition for the equilibrium of the forces in any dimension. This rule is applied when the support reactions are taken into the account for the equilibrium of the body.

41. A couple moment is developed when _______ of the attached member is prevented.

a) Translation
b) Rotation
c) Addition
d) Subtraction
View Answer

Answer: b
Explanation: The development of the couple moment is when there is a prevention of the rotation of the attached member. This is the basic condition for the equilibrium of the couple moments in any dimension. This rule is applied when the couple moments are taken into the account for the equilibrium of the body.

42. We first make equilibrium equations of the body by considering all the three dimensional forces and then the free body diagram is made and solved.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: d
Explanation: We first make the free body diagram and then we make the equilibrium equations to satisfy the given conditions. This helps us to solve the question easily. As this reduces the part of imagination and increases accuracy too.

43. ∑Fx=0, ∑Fy=0 and ∑Fz=0 are vector equations for the three dimensions. They are satisfied when the body is achieved its state of equilibrium.
a) True
b) False

Answer: b
Explanation: The answer is false as the equations asked are scalars. As we make the net sum of the forces along the axis equal to zero. Of course this equation comes from the solving the vector forms, but still the result is a scalar, hence the equations are scalar.

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44. The supports in the 3D are having more than three reaction forces. Because they are having three axis on which the components of the forces need to be zero.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: d
Explanation: As 3D is defined as the three axis system, we have to consider the equilibrium in all the three axis. This will make the equilibrium go on all the axis of the 3D space. And hence will cancel all the forces.

45. The single pin, single bearing and single hinge resist _______
a) Force
b) Couple moments
c) Both force and couple moments
d) Inertia

Answer: c
Explanation: The experiments have founded that the single pin, single bearing and single hinge resist both force and couple moments. This does helps in attaining the equilibrium of the body. Thus proper guiding must be taken during solving the question on the same.

46. If the supports are properly aligned then the reaction forces developed are adequate to support the body.
a) Statement is true only in 2D
b) Statement is true only in 3D
c) Statement is true throughout
d) Statement is true only in 1D

Answer: c
Explanation: This is the basic nature observed during the experiments on the beams an all the support system. The dimension doesn’t affect the equilibrium conditions. The main motto is to achieve the equilibrium. It is achieved by equating the net force equal to zero.

49. If the supports are not properly aligned then the reaction forces developed are adequate to support the body.
a) Statement is true only in 2D
b) Statement is true only in 3D
c) Statement is false throughout
d) Statement is true only in 1D

50. Just like the collinear forces for free body diagrams there are collinear couple and the net moment is taken out from it.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: c
Explanation: Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

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51. The simplification of the forces on the free body diagrams is done as __________
a) A particular system of rule is followed
b) No simplification of the forces is possible
c) The forces are already simplified and don’t need simplification
d) The forces are very tentative quantity on terms of simplification and hence no simplification possible

Answer: a
Explanation: A particular system of the rules is followed that is if the upward direction is taken as positive then the downward direction is taken as negative. This is same as done with the couple in the 2D. That is the forces can be easily simplified. If taken in the vector form then the task is even easier.

53. The system of the collinear and the parallel force in free body diagrams are simplified as _________
a) The simplified collinear force system gives us a net force and the parallel force system gives us a simplified force, and then we add it vectorially
b) Such simplification is not possible
c) The simplification is usually done by not considering the directions of the both
d) The simplification is done by considering the rotations only

Answer: a
Explanation: The simplification is easy. The simplified force system gives us a net force and the parallel force system gives us a simplified force, and then we add it vectorially. Thus the vector addition at the last can be easily done and thus both can be simplified.

54. The couple is a scalar quantity and the force is vector quantity and hence only force can be simplified in free body diagrams.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: a
Explanation: Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

55. The couple is simplified easily by the help of right hand rule in free body diagrams. But the forces simplification is not possible as there is no such system of rules so that the forces can be simplified.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

56. The couple and the other two force systems in free body diagrams can be easily simplified.
a) Statement is wrong
b) Statement is right
c) Statement is right if we remove ‘couple’ part
d) Statement is right if we remove ‘force’ part

Answer: b
Explanation: Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

58. The force and the couple can’t be simplified together as one is the cause and the other is the effect in free body diagrams.
a) The statement is correct and the reason given is also correct
b) The statement is wrong but the reason given is also correct
c) The statement is wrong and the reason given is also wrong
d) The statement is correct but the reason given is also wrong

59. What is a collinear system of forces for free body diagrams?
a) The force system having all the forces parallel to each other
b) The force system having all the forces perpendicular to each other
c) The force system having all the forces emerging from a single point
d) Forces cannot form a collinear system of forces, it is not possible

Answer: c
Explanation: The force system having all the forces emerging from a point is called the collinear system of force. This is a type of system of the force, which is easy in the simplification. This is because as the forces are the vector quantity, the vector math is applied and the simplification is done.

60. The main moto of the free body diagrams is to:
a) To reduce the calculation
b) To add the forces with the couples and take out the total
c) To subtract the forces with the couples and take out the total
d) To multiply the forces with the couples and take out the total

Answer: a
Explanation: The main moto of the free body diagrams is to reduce the calculation. The forces are simplified and the couples too are simplified. This gives us the total force and the total moment acting on the body. This gives us a single value of the respective thing and hence reduces the labour.

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61. The couple moment and the force is divided to get the distance of the axis from the point of action of the force in free body diagrams.
a) True
b) False

Answer: a
Explanation: The couple is the cross product of the force and the perpendicular distance between the forces. And if the division of the both is done than the resulting quantity is the distance only. But care must be taken that the product is the cross product and hence sine angle must be divided too to get the distance.

62. The simplification of the couple is done for free body diagrams on the basis of the:
a) The clockwise of the anti-clockwise rotation sign convention
b) The simplification is not possible
c) The couple is a vector and thus can’t be simplified
d) The couple is a scalar and can’t be simplified

Answer: a
Explanation: The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. If the couple is a vector it can be easily simplified by taking the components.

63. Principle of transmissibility for free body diagrams is:
a) It states that the force acting on the body is a sliding vector
b) It states that the force acting on the body is a rolling vector
c) It states that the force acting on the body is a wedging vector
d) It states that the force acting on the body is a unit vector

Answer: a
Explanation: The principle of transmissibility states that the force acting on the body is a sliding vector. That is it can be applied at any point of the body. It will give the same effect as if applied at any point other than the specific point. Thus the answer.

64. Just like the collinear force system for free body diagrams there is a system of parallel forces.
a) True
b) False

Answer: a
Explanation: There is a system so-called the parallel system of the forces. This is another type of force. The simplification of this type of force is also very easy. This means that the forces in a certain direction are taken as positive and in the other direction is negative and hence the simplification is done.

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Friction

1. ____________ is the phenomena that resist the movement of the two surfaces in contact.
a) Friction
b) Motion
c) Circular movement
d) Rotation

Answer: a
Explanation: The friction is the phenomena that define that there is a resistance which is present there between the two surfaces. The two surfaces are in contact and the friction applies at that surface only, resisting the motion of the surface.

2. The frictional force always acts ____________ to the surface of the application of the friction.
a) Tangential
b) Perpendicular
c) Parallel
d) Normal

Answer: a
Explanation: The friction is the phenomena that defines that there is a resistance which is present there between the two surfaces. This friction is applied tangentially to the surfaces in contact. Thus the main thing is that the forces on both of the surfaces act as a tangential to each other.

3. Dry friction is also called _____________
a) Column Friction
b) Coulomb Friction
c) Dry column friction
d) Surface friction

Answer: b
Explanation: The dry friction is acted upon the surfaces. And they are tangential to each other. As we know the friction is the phenomena that define that there is a resistance which is present there between the two surfaces. The dry friction is also termed as the Coulomb friction as it was given by C.A. Coulomb.

4. Who gave the concept of Dry friction?
a) C.A. Coulomb
b) GA. Coulomb
c) C.P Coulomb
d) Albert Einstein

Answer: a
Explanation: The dry friction is also termed as the Coulomb friction as it was given by C.A. Coulomb. And they are tangential to each other. As we know the friction is the phenomena that defines that there is a resistance which is present there between the two surfaces.

5. At what conditions the dry friction occurs between the surfaces in contact?
a) When there is no lubricating fluid
b) When there is no friction fluid
c) When there is no adhesive fluid
d) When there is no cohesive fluid

Answer: a
Explanation: When there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. Thus as the name suggests dry friction. When there is no liquid present over there the surfaces are going to be said dry only. Thus the term dry friction.

6. The phenomena of horizontal pull and push explain what?
a) Theory of friction
b) Theory of relativity
c) Theory of action
d) Theory of forces

Answer: a
Explanation: As we know that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. This is the phenomena that defines that there is a resistance which is present there between the two surfaces. Thus the pull and push phenomena explain the theory of friction.

7. Theory of friction is explained over a block of weight W. Which of the following is the property of the surface on which block is present?
a) Non-rigid
b) Coloured red
c) Having density in negative
d) The motion of that block is always horizontal

Answer: a
Explanation: The block used to explain the theory of friction is a used in a deformable surface. As we know that the theory of friction says that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. Thus to show the same experiments are done over a non-rigid/deformable surface.

8. The block used to explain the theory of friction is kept over non-deformable surface.
a) True
b) False

Answer: b
Explanation: The block used to explain the theory of friction is used in a deformable surface. As we know that the theory of friction says that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. Thus to show the same experiments are done over a non-rigid/deformable surface.

9. In the explanation of the theory of friction, the block used to have an assumption. That is the upper portion of the block is considered to be rigid.
a) True
b) False

Answer: b
Explanation: The block used to explain the theory of friction is placed on a deformable surface. As we know that the theory of friction says that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. Thus to show the same, experiments are done over a non-rigid/deformable surface which is having a rigid shape.

10. The free body diagram used to explain the theory of dry friction is having ___________ distribution of both the normal forces and frictional surface.
a) Uneven
b) Even
c) Uniform
d) Equal

Answer: a
Explanation: As we know that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. This is the phenomena that define that there is a resistance which is present there between the two surfaces. Thus the pull and push phenomena explain the theory of friction. Thus the free body diagrams are having an uneven distribution of the forces.

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11. For equilibrium the normal forces acts in which direction in the free body diagrams?
a) Vertically Upward
b) Vertically Downward
c) Horizontally Right
d) Horizontally Left

Answer: a
Explanation: As the loads are being acting in the downward direction. Thus to make the forces balance, the normal forces act in the vertically upward direction. As we know that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. This friction magnitude is taken out from these normal forces.

12. What is not the condition for the equilibrium in free body diagram for calculation of the normal forces?
a) ∑Fx=0
b) ∑Fy=0
c) ∑Fz=0
d) ∑F≠0

Answer: d
Explanation: For the equilibrium in the three dimensional system of axis we have all the conditions true as, ∑Fx=0, ∑Fy=0 and ∑Fz=0. Also we have the summation of the forces equal to zero. Which is not a non-zero value.

13. We first make equilibrium equations of the body by considering all the three dimensional forces acting on the section chosen and then the free body diagram is made and solved.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

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15. For making the equilibrium equations the normal forces acts in which direction in the free body diagrams?
a) Vertically Upward
b) Vertically Downward
c) Horizontally Right
d) Horizontally Left

Answer: a
Explanation: As the loads are acting in the downward direction. Thus to make the forces balance, the normal forces act in the vertically upward direction. As we know that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. This friction magnitude is taken out from these normal forces.

16. Which one is not the condition for the equilibrium in free body diagram for calculation of the normal forces, consider all forces to be straight and linear?
a) ∑Fx=0
b) ∑Fy=0
c) ∑Fz=0
d) ∑F≠0

17. We show the net forces by the help of __________ forces.
a) Rotational
b) Linear
c) Helical
d) Resultants

Answer: d
Explanation: The net forces acting on the body is shown with the help of the resultant forces. This is because the resultant forces have the sum of all the forces which are acting in the direction which is same. Thus the resultant forces are used to show the net forces acting in the body.

18. There are main two types of forces which are being stated in the free body diagram, they are generally the resultant forces which are being acted over the body. Which are they?
a) Normal and Frictional
b) Normal and Vertical
c) Vertical and Frictional
d) Normal and Fractional

Answer: a
Explanation: The net forces acting on the body is shown with the help of the resultant forces. There are two types, first the frictional and the second is the normal. This is because the resultant forces have the sum of all the forces which are acting in the direction which is same.

19. In the problems regarding the friction and normal force calculations, there is no scope of the two force and three force systems.
a) True
b) False

Answer: b
Explanation: The two and three force member system can be acted upon the body even if there are friction calculations involved. The main thing is that the frictional forces are the phenomena in which there is a resistance between the surfaces. And the resistance magnitude is given by those calculations. So if two or three system does comes, it has no effect.

20. There is the application of the Newton’s third law of motion in the free body diagrams of the friction calculations.
a) True
b) False

Answer: a
Explanation: There is some calculations involved in which we have to make use of Newton’s third law of motion. The requirement of the third law is important in the equilibrium of the body. The body particles are in the equilibrium and are thus facing the forces and to be in the equilibrium they also react and apply the opposite force and thus the third law of newton.

21. As we are using vector math to solve for the unknown forces in the free body diagrams, what is k.i?
a) 0
b) 1
c) -1
d) ∞

Answer: a
Explanation: As the dot product of only the same Cartesian component is unity, i.e. i.i = 1 and j.j =1, rest all remaining dot product will give 0(i.j = 0 and j.k = 0). Cross product of the same plane vectors always give zero. This is generally done because the normal forces are perpendicular to the surfaces of action of the friction.

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21. The three force system can also be in the equilibrium if:
a) All the forces are parallel to each other heading towards the same direction
b) The force components cancel each other
c) The forces are very small in magnitude
d) The forces are very huge in magnitude

Answer: b
Explanation: Even if the forces components cancels each other than the body is said to be in equilibrium. Also, it should satisfy whether the moments caused by the forces are equal to zero or not. This means that we need to take components of the normal and frictional forces so as to make the desired calculations.

22. The normal forces and the forces of friction are collinear.
a) True
b) False

Answer: b
Explanation: They are not collinear. They are just acting perpendicular or parallel to the surface of action. Thus they are not even on the same plane. So as to make the calculations proper we need to see the same and then apply the equations.

25. What does the moment of the force measured in the rolling of the body?
a) The tendency of rotation of the body along any axis
b) The moment of inertia of the body about any axis
c) The couple moment produce by the single force acting on the body
d) The total work done on the body by the force

Answer: a
Explanation: The moment of the force measures the tendency of the rotation of the body along any axis, whether it be the centroid axis of the body, or any of the outside axis. The couple moment is produced by two forces, not by a single force. The total work done is the dot product of force and distance not the cross.

27. If a car is moving forward, what is the direction of the moment of the moment caused by the rolling of the tires, assume non slippery surface?
a) It is heading inwards, i.e. the direction is towards inside of the car
b) It is heading outwards, i.e. the direction is towards outside of the car
c) It is heading forward, i.e. the direction is towards the forward direction of the motion of the car
d) It is heading backward, i.e. the direction is towards back side of the motion of the car

28. The moment of the force is the product of the force and the perpendicular distance of the axis and the point of action of the force. Is this also true for rolling?
a) True
b) False

29. For the rolling of the body the calculation of the moment of the force about the axis of rolling, the cross product table, i.e. the 3X3 matrix which is made for doing the cross product having 3 rows, contains three elements. Which are they from top to bottom?
a) Axis coordinates, point coordinates, and the force coordinates
b) Point coordinates, axis coordinates, and the force coordinates
c) Axis coordinates, force coordinates, and the point coordinates
d) Force coordinates, point coordinates, and the axis coordinates

Answer: a
Explanation: The 3X3 matrix which is being made is having axis coordinates, point coordinates and the force coordinates. They are from top to bottom place. The order cannot be changed. Or if changed then one needs to apply the negative sign appropriately. Negative because the directions get reversed.

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31. In rolling, there is the involvement of the vector math. So for rolling which of the following is correct? (For A representing the vector representation of the axis of rotation, r the radius vector and F the force vector)
a) A.(rxF)
b) Ax(rxF)
c) A.(r.F)
d) Fx(r.F)

Answer: a
Explanation: The correct form of the equation is given by A.(rxF). Where A represents the vector representation of the axis of rotation, r the radius vector and F the force vector. This is usually done for determining the moment of the force about the axis. That is if the body is being rotated by the force about an axis.

32. The ___________ forces do not cause the rotation/rolling of the body if the rotation is considered in about the axis of the body or the centroid axis of the body.
a) Non-concurrent
b) Concurrent
c) Parallel
d) Non-Parallel

Answer: b
Explanation: The concurrent forces are the which are somewhere touching the axis of rotation. If any of the force is touching that axis, that force is not considered or is insufficient to cause a rotation. If a force is concurrent then the perpendicular distance of the force from the line of axis is zero, thus no rotation. As we know rotation is caused by a moment.

33. For the rolling of the body right handed coordinate system means (consider the mentioned axis to be positive)?
a) Thumb is z-axis, fingers curled from x-axis to y-axis
b) Thumb is x-axis, fingers curled from z-axis to y-axis
c) Thumb is y-axis, fingers curled from x-axis to z-axis
d) Thumb is z-axis, fingers curled from y-axis to x-axis

Answer: a
Explanation: As right handed coordinate system means that you are curling your fingers from positive x-axis towards y-axis and the thumb which is projected is pointed to the positive z-axis. Thus visualizing the same and knowing the basic members of axis will not create many problems. The right handed coordinate system is universal throughout.

34. In the equation Wa/r generally used in the rolling frictional calculations, what does each stands for?
a) P is the force, W is weight of the body, r radius and a coefficient of rolling friction all in normal powers
b) P is the force in nano Newton, W is weight of the body, r radius and a coefficient of rolling friction
c) P is the force, W is weight of the body in kg, r radius and a coefficient of rolling friction
d) P is the force, W is weight of the body, r radius cm and a coefficient of rolling friction

Answer: a
Explanation: The rolling of the cylinder is termed as perfect rolling only when the cylinder is rolling at a constant velocity. Also, the rolling should be along the rigid surface. The normal forces are acting perpendicular to the surface of the rolling. And for rolling equation, Wa/r is generally used.

35. Which statement is correct about the vector F acting parallel to the direction of the motion of the rolling body?
a) F= Fcos β + Fcos α + Fcosγ
b) F= Fsin β + Fcos α + Fcosγ
c) F= Fcos β + Fsin α + Fcosγ
d) F= Fcos β + Fcos α + Fsinγ

36. What if the moment of the force calculated about the axis of rolling is negative?
a) It means that the force is applied in the opposite direction as imagined
b) It means that the direction of the motion is in the opposite sense as imagined
c) It means that the radius vector is in the opposite sense as imagined
d) Such calculation means that the calculations are wrongly done

Answer: b
Explanation: It means that the direction of the rolling is in the opposite sense as imagined. We can’t say about the direction of the force or the direction of the radius vector. But yes we can say about the direction of the rolling as it is the thing which is going to be calculated. Rest all the parts are fixed. They can’t be altered.

37. In the equation A.(rxF) the r is heading from ______________ and ending at _____________
a) Axis of rolling, Force vector
b) Axis of rolling, Force vector’s point of action on the body
c) Force vector, Axis of rolling
d) Force vector’s point of action on the body, Axis of rolling

Answer: b
Explanation: It is the radius vector. The radius vector is always from the axis of rolling to the point of action of the force on the body. Which means that the radius vector is not on any point on the force vector. Rather it ending at the point on the force vector, where it is being in contact of the body.

39. Rotation is termed as rolling when _______
a) Constant velocity of rolling
b) Variable velocity of rolling
c) Constant speed of rolling
d) Variable speed of rolling

40. The pivots are generally used in __________
a) Belts
b) Columns
c) Beams
d) Machines

Answer: d
Explanation: The pivots are being used in the machines. They are used as to support the loadings. This means that the more the pivots the more is the stable the structure. Thus the use of pivots.

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42. The collar bearings are generally used in __________
a) Belts
b) Columns
c) Beams
d) Machines

Answer: d
Explanation: The collar bearings are being used in the machines. They are used as to support the loadings. This means that the more the collar bearings the more is the stable the structure. Thus the use of collar bearings.

43. The pivots and collar bearings are used as to support the axial load on the rotating shaft.
a) False
b) True

Answer: b
Explanation: The collar bearings and pivots are being used in the machines. They are used as to support the loadings. This means that the more the collar bearings or pivots more is the stable the structure. Thus used as a supporting system to the shafts.

44. A phenomena is there in these collar bearings and pivots, which is very helpful in the supporting of the machines, and that is _____________
a) Column Friction
b) Coulomb Friction
c) Dry column friction
d) Surface friction

Answer: b
Explanation: The dry friction is acted upon the surfaces. And they are tangential to each other. As we know the friction is the phenomena that defines that there is a resistance which is present there between the two surfaces. This Coulomb friction is also known as dry friction.

45. At what conditions does the Coulomb friction occur between the surfaces in contact of collar bearings or pivots?
a) When there is no lubricating fluid
b) When there is no friction fluid
c) When there is no adhesive fluid
d) When there is no cohesive fluid

46. We first make equilibrium equations of the sections involving the collar bearings or pivots by considering all the three dimensional forces acting on the section chosen and then the free body diagram is made and solved.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: d
Explanation: We first make the free body diagram of collar bearings or pivots and then we make the equilibrium equations to satisfy the given conditions. This helps us to solve the question easily. As this reduces the part of imagination and increases accuracy too.

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46. To know the rotations involved in the disks we use right handed coordinate system, in that system which of the following is followed (consider the mentioned axis to be positive)?
a) Thumb is z-axis, fingers curled from x-axis to y-axis
b) Thumb is x-axis, fingers curled from z-axis to y-axis
c) Thumb is y-axis, fingers curled from x-axis to z-axis
d) Thumb is z-axis, fingers curled from y-axis to x-axis

47. In the calculations involving the collar bearings and the pivot bearings, we use cross product. In that mathematically, for two vectors A and B of any magnitude, the cross product of both, i.e. AxB = given by:
a) |A||B|sinØ
b) |A||B|
c) |A||B|cosØ
d) |A||B|sin(180°+Ø)

Answer: a
Explanation: The cross product of two vectors gives a vector which is perpendicular to both of the vectors. And the mathematic equation for the same is given by: |A||B|sinØ. And the dot product of the same by any of the other two vectors will give the answer zero, as perpendicular. The cross product is the same for all the systems of its application.

48. In the calculations of the bearings, we often use vector math. So for those systems which of the following is true?
a) i x i =1
b) j x i = -j
c) k x j = -i
d) k x k = 1

Answer: c
Explanation: As the mathematic equation for the cross product is having a cosine function in it, in which the angle used in the function is the angle between the vectors. Thus the cross product will be zero if the angle between them is 90. The vector math system remains the same for every system in the environment.

49. The moment is the cross product of which two vectors in the calculations of the pivots and disks?
a) Force and Radius vectors
b) Radius and Force vectors
c) Force and Radius scalars
d) Radius and Force scalars

Answer: b
Explanation: The cross product needs to take in the proper sequence. If not taken then the answer is just the opposite of the true answer. That’s why, the answer is not the Force and Radius vectors, but the Radius and Force vectors. Because the moment has its direction, as many of the cross products have, and thus precaution needs to be taken.

50. Principle of transmissibility is somehow applied to the collar bearings. It states that:
a) It states that the force acting on the body is a sliding vector
b) It states that the force acting on the body is a rolling vector
c) It states that the force acting on the body is a wedging vector
d) It states that the force acting on the body is a unit vector

Answer: a
Explanation: Principle of transmissibility states that the force acting on the body is a sliding vector. That is it can be applied at any point of the body. It will give the same effect as if applied at any point other that the specific point. Thus the answer.

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51. Coplanar forces are not easily simplified in the simplification of the force and couple system in the calculations of forces in the pivots and collar bearings.
a) True
b) False

Answer: b
Explanation: The coplanar forces can be easily simplified in the simplification of the force and couple system. This is not only for the coplanar system of the forces but for any of the dimension vector. Which means the answer is false.

Answer: a
Explanation: As we know that the moment is the cross product of the force and the distance between the point of contact of the force and the point about which moment needs to be calculated. Thus forming the distance vector and then crossing it with the force will give us the answer. Remember force also needs to be in the vector form for doing the cross product.

53. A ____________ is a simple machine that is used as to transfer applied forces into much larger forces.
a) Wedge
b) Beam
c) Pillar
d) Bridges

Answer: a
Explanation: The main thing about the wedges is that a wedge is a simple machine that is used as to transfer applied forces into much larger forces. This means that the wedges are the means of force transfer. This machine is very useful in the industries, and it has a wide application.

54. Wedges are used to transfer heavy loads.
a) True
b) False

55. The blocks of heavy weights are being able to lift from the help of the wedges.
a) True
b) False

Answer: a
Explanation: The main thing about the wedges is that the wedge is a simple machine that is used as to transfer applied forces into much larger forces. This means that the wedges are the means of force transfer. This machine is very useful in the industries, and it has a wide application.

56. The normal force exerted by the surface of the wedge is normal to the surface of the ________
a) Base of the wedge
b) Base of the body residing over it
c) Base of the body just neighbour to the wedge
d) Earth’s surface

Answer: b
Explanation: As we know the normal forces act perpendicular to the surfaces of the body kept over the wedges. Thus the normal force exerted by the surface of the wedge is normal to the surface of the base of the body kept over the wedge. The wedges are very useful in the industries, and it has a wide application.

57. Which one is not the condition for the equilibrium in free body diagram for calculation of the normal forces along the body kept over the wedge, consider all forces to be straight and linear?
a) ∑Fx=0
b) ∑Fy=0
c) ∑Fz=0
d) ∑F≠0

58. The coefficient of friction between the body being slided over the wedge and the wedge surface is generally determined by ____________
a) Written over the Body
b) Experiments
c) Weighing the body
d) Measuring length of the body

Answer: b
Explanation: The coefficient of the friction is generally determined by the help of experiments. Many experiments are done on the body. Try and error methods are involved. And the final observations are being taken out. Then average of all the final answers resulted in the experiments is done.

59. When does the two wedge system is termed as self-locking system?
a) If friction forces hold the block in plane
b) If friction forces doesn’t hold the block in plane
c) If friction forces hold the block in phase
d) If friction forces doesn’t hold the block in phase

Answer: a
Explanation: If friction forces hold the block in plane the two wedge system is termed as self-locking system. This is generally the concept used to lift up the boxes and then it is also used to make the very heavy works easy. Thus the wedges are very useful in the industries, and it has a wide application.

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61. In the free-body diagrams involving the wedges we have the use of vector math, so for two vectors A and B, what is A.B (if they have angle α between them)?
a) |A||B| cosα
b) |A||B|
c) √(|A||B|) cosα
d) |A||B| sinα

Answer: a
Explanation: The dot product of the two vectors is always the product of the magnitudes of the two forces and the cosine of the angle between them. We need to consider the triangle and then accordingly apply the trigonometry. This is one of the ways of resolving the components.

62. What is j.j?
a) 0
b) 1
c) -1
d) ∞

Answer: b
Explanation: As the dot product of only the same Cartesian component is unity, i.e. i.i = 1 and j.j =1, rest all remaining dot product will give 0(i.j = 0 and j.k = 0). Cross product of the same plane vectors always give zero. And dot product of the same plane vector gives a scalar quantity.

63. Sometimes in the calculations involving the wedges, there are situations when there is a toppling effect on the body. In that, if the net moment of the body is zero that means the distance between the force and the rotational axis is zero.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: c
Explanation: The net moment of the body is zero that doesn’t means that the distance between the force and the rotational axis is zero. This means moments caused by different forces cancels out. If this happens there is no motion of the body along with any direction and hence the body is said to be in equilibrium.

64. In the simplification of the forces applied in the wedges net force acts at the ___________ of the loading body.
a) Centroid
b) The centre axis
c) The corner
d) The base

Answer: a
Explanation: In the simplification of the loading system the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading.

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Kinematics of Particle

1. The unit of linear acceleration is
a) kg-m
b) m/s
c) m/s²
d) rad/s²

Answer: c
Explanation: Linear acceleration is defined as the rate of change of linear velocity of a body with respect to the time.
i.e a = v/t
and unit of velocity is m/s
so, unit of linear acceleration becomes m/s².

2. The angular velocity (in rad/s) of a body rotating at N r.p.m. is
a) π N/60
b) 2 π N/60
c) π N/120
d) π N/180

Answer: b
Explanation: Angular velocity is defined as the rate of change of angular displacement with respect to time. It is usually expressed by a Greek letter ω (omega).
Mathematically, angular velocity,
ω =dθ/dt
If a body is rotating at the rate of N r.p.m. (revolutions per minute), then its angular velocity,
ω = 2πΝ / 60 rad/s

3. The linear velocity of a body rotating at ω rad/s along a circular path of radius r is given by
a) ω.r
b) ω/r
c) ωs².r
d) ωs²/r

Answer: a
Explanation: If the displacement is along a circular path, then the direction of linear velocity at any instant is along the tangent at that point.
therefore, the linear velocity will be
ω.r

4. When a particle moves along a straight path, then the particle has
a) tangential acceleration only
b) centripetal acceleration only
c) both tangential and centripetal acceleration
d) none of the mentioned

Answer: a
Explanation: The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known as tangential component of acceleration or tangential acceleration.

5. When a particle moves with a uniform velocity along a circular path, then the particle has
a) tangential acceleration only
b) centripetal acceleration only
c) both tangential and centripetal acceleration
d) none of the mentioned

Answer: b
Explanation: The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path is known as normal component of the acceleration or normal acceleration. It is also called radial or centripetal acceleration.

6. When the motion of a body is confined to only one plane, the motion is said to be
a) plane motion
b) rectilinear motion
c) curvilinear Motion
d) none of the mentioned

Answer: a
Explanation: When the motion of a body is confined to only one plane, the motion is said to be plane motion. The plane motion may be either rectilinear or curvilinear.

7. _______________ is the simplest type of motion and is along a straight line path.
a) plane motion
b) rectilinear motion
c) curvilinear Motion
d) none of the mentioned

Answer: b
Explanation: Rectilinear Motion is the simplest type of motion and is along a straight line path. Such a motion is also known as translatory motion.

8. _________________ is the motion along a curved path.
a) plane motion
b) rectilinear motion
c) curvilinear Motion
d) none of the mentioned

Answer: c
Explanation: Curvilinear Motion is the motion along a curved path. Such a motion, when confined to one plane, is called plane curvilinear motion.

9. Displacement of a body is a ___________ quantity.
a) scalar
b) vector
c) scalar and vector
d) none of the mentioned

Answer: b
Explanation: The displacement of a body is a vector quantity, as it has both magnitude and direction. Linear displacement may, therefore, be represented graphically by a straight line.

10. A train covers 60 miles between 2 p.m. and 4 p.m. How fast was it going at 3 p.m.?
a) 60 mph
b) 30 mph
c) 40 mph
d) 50 mph

Answer: b
Explanation: The speed is traveled distance (60 miles) divided by traveled time (4pm – 2pm = 2hours):60 miles/ 2 hours = 30 mph

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11. A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. What is its angular acceleration?
a) 10.475 rad/s²
b) 12 rad/s²
c) 14 rad/s²
d) 15 rad/s²

Answer: a
Explanation: Solution. Given : N₀ = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s
Angular acceleration
Let α = Angular acceleration in rad/s²
We know that
ω = ω₀ + α.t
or 209.5 = 0 + α × 20
or α = 209.5 / 20 = 10.475 rad/s²

12. A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. How many revolutions does the wheel make in attaining the speed of 2000 r.p.m.?
a) 400
b) 300
c) 333.4
d) 200

Answer: c
Explanation: Solution. Given : N₀ = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s
We know that the angular distance moved by the wheel during 2000 r.p.m. (i.e. when ω = 209.5 rad/s),
θ = (ω₀ + ω )t/2
= (0 + 209.5)20/2
= 2095 rad
Since the angular distance moved by the wheel during one revolution is 2π radians, therefore number of revolutions made by the wheel,
n = θ /2π = 2095/2π = 333.4

13. The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known
a) tangential component
b) normal component
c) parallel component
d) none of the mentioned

Answer: a
Explanation: The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known tangential component.
The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as normal component.

14. The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as
a) tangential component
b) normal component
c) parallel component
d) none of the mentioned

Answer: b
Explanation: The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known tangential component.
The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as normal component.

15. When a particle moves along a straight path, then the radius of curvature is
a) infinitely small
b) zero
c) infinitely great
d) none of the mentioned

Answer: c
Explanation: When a particle moves along a straight path, then the radius of curvature is infinitely great. This means that v²/r is zero.

16. When a particle moves with a uniform velocity, then dv/dt will be
a) infinitely small
b) zero
c) infinitely great
d) none of the mentioned

Answer: b
Explanation: When a particle moves with a uniform velocity, then dv/dt will be zero. In other words, there will be no tangential acceleration; but the particle will have only normal or radial or centripetal acceleration.

17. A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at the beginning of the interval ?
a) 188.6 m/s
b) 235.5 m/s
c) 300 m/s
d) 400 m/s

Answer: a
Explanation: Given : r = 1.5 m ; N₀ = 1200 r.p.m. or ω₀ = 2 π × 1200/60 = 125.7 rad/s ;
N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s
Linear velocity at the beginning
We know that linear velocity at the beginning,
v₀ = r . ω₀ = 1.5 × 125.7 = 188.6 m/s

18. A horizontal bar 1.5 metres long and of small cross-section rotates about a vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at end of the interval?
a) 188.6 m/s
b) 235.5 m/s
c) 300 m/s
d) 400 m/s

Answer: b
Explanation: Given : r = 1.5 m ; N₀ = 1200 r.p.m. or ω₀ = 2 π × 1200/60 = 125.7 rad/s ;
N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s
Linear velocity at the end of 5 seconds
We also know that linear velocity after 5 seconds,
v₅ = r . ω = 1.5 × 157 = 235.5 m/s

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Kinematics of Rigid Body

1. Which is the false statement about the properties of instantaneous centre?
a) at the instantaneous centre of rotation, one rigid link rotates instantaneously relative to another for the configuration of mechanism considered
b) the two rigid links have no linear velocities relative to each other at the instantaneous centre
c) the two rigid links which have no linear velocity relative to each other at this centre have the same linear velocity to the third rigid link
d) the double centre can be denoted either by O₂₁ or O₁₂, but proper selection should be made

Answer: d
Explanation: The following properties of the instantaneous centre are important from the subject point of view :
1. A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.
2. The two rigid links have no linear velocity relative to each other at the instantaneous centre. At this point (i.e. instantaneous centre), the two rigid links have the same linear velocity relative to the third rigid link. In other words, the velocity of the instantaneous centre relative to any third rigid link will be same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.

2. Instantaneous center of rotation of a link in a four bar mechanism lies on
a) right side pivot of this link
b) left side pivot of this link
c) a point obtained by intersection on extending adjoining links
d) none of the mentioned

Answer: c
Explanation: None.

3. The total number of instantaneous centers for a mechanism of n links is
a) n(n – 1)/2
b) n
c) n – 1
d) n(n – 1)

Answer: a
Explanation: The number of pairs of links or the number of instantaneous centres is the number of combinations of n links taken two at a time. Mathematically, number of instantaneous centres,
N = n(n – 1)/2.

4. The number of links and instantaneous centers in a reciprocating engine mechanism are
a) 4,4
b) 4,5
c) 5,4
d) 4,6

Answer: d
Explanation: First of all, determine the number of instantaneous centres (N) by using the relation
N = n(n – 1)/2
In present case, N = 4(4 – 1)/2 (n = 4)
= 6.

5. According to Kennedy’s theorem, if three bodies have plane motions, their instantaneous centres lie on
a) a triangle
b) a point
c) two lines
d) a straight line

Answer: d
Explanation: The Aronhold Kennedy’s theorem states that if three bodies move relatively to each other, they have three instantaneous centres and lie on a straight line.

6. In a rigid link OA, velocity of A w.r.t. O will be
a) parallel to OA
b) perpendicular to OA
c) at 45⁰ to OA
d) along AO

Answer: b
Explanation: None.

7. Two systems shall be dynamically equivalent when
a) the mass of two are same
b) c.g. of two coincides
c) M.I. of two about an axis through c.g. is equal
d) all of the mentioned

Answer: d
Explanation: None.

8. A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to
a) OP
b) OQ
c) PQ
d) line in between OP and OQ

Answer: c
Explanation: A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to PQ.
The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line joining the corresponding points.

9. The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line
a) joining the corresponding points
b) perpendicular to line
c) at 45⁰ to line
d) none of the mentioned

Answer: a
Explanation: A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to PQ.
The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line joining the corresponding points.

10. The absolute acceleration of any point P in a link about center of rotation O is
a) along PO
b) perpendicular to PO
c) at 45⁰ to PO
d) none of the mentioned

Answer: d
Explanation: The coriolis component of acceleration is always perpendicular to the link.

11. Angular acceleration of a link can be determined by dividing the
a) centripetal component of acceleration with length of link
b) tangential component of acceleration with length of link
c) resultant acceleration with length of link
d) all of the mentioned

Answer: b
Explanation: The angular acceleration of the link AB is obtained by dividing the tangential components of the acceleration of B with respect to A to the length of the link.

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12.What is the radius of gyration of a uniform rod whose length is L and passes through the centre of mass
(a) L3√
(b) L2√
(c) L23√
(d) L212
Answer: (c) L23√

13.By what percentage does the kinetic energy increase, if the linear momentum is increased by 50%
(a) 25%
(b) 50%
(c) 100%
(d) 125%
Answer: (d) 125%

14.What is the angular momentum vector in an orbital motion?
(a) The vector is perpendicular to the orbital plane
(b) The vector is along the radius vector
(c) The vector is parallel to the linear momentum
(d) The vector is in the orbital plane
Answer: (a) The vector is perpendicular to the orbital plane

15.What is the acceleration of the rolling sphere at the centre of the plane with inclination, Ө to the horizontal?
(a) Zero
(b) Less than g sin Ө
(c) Greater than g sin Ө
(d) g sin Ө
Answer: (b) Less than g sin Ө

16.On which of the following factor does the moment of inertia of an object not depend upon
(a) Axis of rotation
(b) Angular velocity
(c) Distribution of mass
(d) Mass of an object
Answer: (b) Angular velocity

17.What is the frictional force of a round object with mass M and radius R which rolls down the inclined plane without slipping along the way
(a) There is a decrease in the rotational motion
(b) There is a decrease in the rotational and translational motion
(c) There is a conversion of translational motion into rotational motion
(d) Kinetic energy is converted into heat
Answer: (c) There is a conversion of translational motion into rotational motion

18.When the torque acting on the system is zero, which of the following is constant?
(a) Linear impulse
(b) Linear momentum
(c) Force
(d) Angular momentum
Answer: (d) Angular momentum

19.The angular momentum of a rigid body is L and its kinetic energy is halved. What happens to its angular momentum?
(a) L
(b) 2L
(c) L2
(d) L4
Answer: (c) L4

20.Consider two objects a disk and a sphere that has the same radius but different masses which roll down the two inclined planes with the same altitude and length. Out of the two objects, which one gets to the bottom of the plane first?
(a) It is dependent on the masses of the objects
(b) Disk
(c) Sphere
(d) Both reach at the same time
Answer: (c) Sphere

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21.What does L22I represent?
(a) Power
(b) The torque of a particle
(c) The potential energy of a particle
(d) The rotational kinetic energy of a particle
Answer: (d) The rotational kinetic energy of a particle

22.The motion of planets in the solar system is an example of conservation of
(a)Energy
(b) Linear momentum
(c) Angular momentum
(d) Mass
Answer: (c) Angular momentum

23When does the moment of inertia of a body come into the picture?
(a) When the motion is rotational
(b) When the motion is linear
(c) When the motion is along a curved path
(d) None of the above
Answer: (a) When the motion is rotational

24.What is the radius of gyration of a uniform rod whose length is L and passes through the centre of mass
(a) L3√
(b) L2√
(c) L23√
(d) L212
Answer: (c) L23√

25.By what percentage does the kinetic energy increase, if the linear momentum is increased by 50%
(a) 25%
(b) 50%
(c) 100%
(d) 125%
Answer: (d) 125%

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26.What is the angular momentum vector in an orbital motion?
(a) The vector is perpendicular to the orbital plane
(b) The vector is along the radius vector
(c) The vector is parallel to the linear momentum
(d) The vector is in the orbital plane
Answer: (a) The vector is perpendicular to the orbital plane

27.What is the acceleration of the rolling sphere at the centre of the plane with inclination, Ө to the horizontal?
(a) Zero
(b) Less than g sin Ө
(c) Greater than g sin Ө
(d) g sin Ө
Answer: (b) Less than g sin Ө

28.On which of the following factor does the moment of inertia of an object not depend upon
(a) Axis of rotation
(b) Angular velocity
(c) Distribution of mass
(d) Mass of an object
Answer: (b) Angular velocity

29.What is the frictional force of a round object with mass M and radius R which rolls down the inclined plane without slipping along the way
(a) There is a decrease in the rotational motion
(b) There is a decrease in the rotational and translational motion
(c) There is a conversion of translational motion into rotational motion
(d) Kinetic energy is converted into heat
Answer: (c) There is a conversion of translational motion into rotational motion

30.When the torque acting on the system is zero, which of the following is constant?
(a) Linear impulse
(b) Linear momentum
(c) Force
(d) Angular momentum
Answer: (d) Angular momentum

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31.The angular momentum of a rigid body is L and its kinetic energy is halved. What happens to its angular momentum?
(a) L
(b) 2L
(c) L2
(d) L4
Answer: (c) L4

32.Consider two objects a disk and a sphere that has the same radius but different masses which roll down the two inclined planes with the same altitude and length. Out of the two objects, which one gets to the bottom of the plane first?
(a) It is dependent on the masses of the objects
(b) Disk
(c) Sphere
(d) Both reach at the same time
Answer: (c) Sphere

33.What does L22I represent?
(a) Power
(b) The torque of a particle
(c) The potential energy of a particle
(d) The rotational kinetic energy of a particle
Answer: (d) The rotational kinetic energy of a particle

34.The motion of planets in the solar system is an example of conservation of
(a) Energy
(b) Linear momentum
(c) Angular momentum
(d) Mass
Answer: (c) Angular momentum

35.When does the moment of inertia of a body come into the picture?
(a) When the motion is rotational
(b) When the motion is linear
(c) When the motion is along a curved path
(d) None of the above
Answer: (a) When the motion is rotational

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Kinetics of a Particle

1. How is a jet plane able to fly in the air?
The thrust of the jet plane compensates the force of gravity
The weight of the air is the weight of the plane
The force of gravity doesn’t act on bodies moving with high speed
The flow of the air around the wings cause an upward force which compensates for the force of gravity
Answer: (a) The thrust of the jet plane compensates the force of gravity

2. A player catches a ball of mass 150 gm moving at a rate of 20 m/s. If the process of catching is to be completed in 0.1 sec. What is the force exerted by the ball on the hands of the player?
3000 N
300 N
30 N
0.3 N
Answer: (c) 30 N

3. When a force acts on a ball of mass 150 g for 0.1 sec, it produces an acceleration of 20 m/s². What is the value of this impulsive force?
0.5 N-s
0.1 N-s
0.3 N-s
1.2 N-s
Answer: (c) 0.3 N-s

4. What is the motion of the rocket based on?
Mass
Linear Momentum
Kinetic Energy
Angular Momentum
Answer: (b) Linear Momentum

5. Which of the following is momentum closely related to?
Impulse
Power
Force
Kinetic Energy
Answer: (a) Impulse

6. Rocket Engines lift rocket from the earth surface because the hot gas with high velocity
Push against the air
Push against the earth
Heat up the air which lifts the rocket
React against the rocket and push it up
Answer: (d) React against the rocket and push it up

7. A bullet of mass 5 gm is fired from a gun of mass 5 kg. What is the velocity of the muzzle if the recoil velocity is 500 m/s.
500 m/s
5 m/s
50 m/s
0.5 m/s
Answer: (d) 0.5 m/s

8. A rope of length 5 m is kept on a frictionless surface and a force of 5 N is applied to one of its ends. What is the tension in the rope at 1 m from this end?
1 N
4 N
3 N
5 N
Answer: (b) 4 N

9. A wagon weighing 1000 kg moves 50 km/h on smooth rails. Later, a mass of 250 kg is placed in the wagon. What is the velocity with which it moves?
20 km/hr
50 km/hr
40 km/hr
2.5 km/hr
Answer: (c) 40 km/hr

10. An iron ball having a mass of 100 g with a velocity of 10 m/s collides with the wall at an angle of 300 and rebounds with the same angle. If the period of contact between the wall and the ball is 0.1 second. What is the force experienced by the ball?
0.1 N
1 N
10 N
100 N
Answer: (c) 10 N

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11. Work done in raising a box depends on
How fast it is raised
The strength of the man
The height by which it is raised
None of the above
Answer: (c) The height by which it is raised

12.A light and a heavy body have equal momenta. Which one has greater kinetic energy?
The light body
The heavy body
The kinetic energy is equal
Data is incomplete
Answer: (a) The light body

13.A body at rest may have
Energy
Momentum
Speed
Velocity
Answer: (a) Energy

14. If the momentum of a body is increased n times, its kinetic energy increase
n times
2n times
n³ times
n² times
Answer: (d) n² times

15.When work is done on a body by an external force, its
kinetic energy increases
potential energy increases
Both kinetic energy and potential energy increases
Sum of the kinetic energy and potential energy remains constant
Answer: (c) Both kinetic energy and potential energy increases

16.If the K.E of a body is increased by 300% its momentum will increase by
100%
150%
200%
175%
Answer: (a) 100 %

17.A light and a heavy body have equal kinetic energy. Which one has a greater momentum?
The light body
The heavy body
Both have equal momentum
It is not possible to say anything without additional information
Answer: (b) The heavy body

18.If the linear momentum is increased by 50% the kinetic energy will increase by
50%
100%
125%
25%
Answer: (c) 125%

19.If the stone is thrown up vertically and return to the ground, its potential energy is maximum
During the upward journey
At the maximum height
During the return journey
At the bottom
Answer: (b) At the maximum height

20.The energy stored in wound watch spring is
K.E
P.E
Heat Energy
Chemical Energy
Answer: (b) P.E

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21. A body can have momentum without energy.
a) True
b) False

Answer: b
Explanation: If a body has momentum, it must be in motion and consequently possess kinetic energy. Therefore a body cannot have momentum without energy.

22. Comets mover around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every orbit of the comet is zero. Why?
a) The gravitational force is conservative, hence work done is zero
b) The gravitational force is non-conservative, hence work done is zero
c) Energy is absent, hence work done is zero
d) Force is in negative direction

Answer: a
Explanation: The gravitational force acting on the comet is a conservative force. The work done by a conservative force is equal to the negative of the change in potential energy. Over a complete orbit of any shape, there is no change in potential energy of the comet. Hence no work is done by the gravitational force on the comet.

23. An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. As it comes closer and closer to earth, its speed ___________
a) Decreases progressively
b) Remains constant
c) Becomes non-uniform
d) Increases progressively

Answer: d
Explanation: As the satellite comes closer to the earth, its potential energy decreases. As the sum of kinetic energy and potential energy remains constant, the kinetic energy and the velocity of the satellite increase. But the total energy of the satellite goes on decreasing due to the loss of energy against friction.

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24. In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.
a) True
b) False

Answer: a
Explanation: In an inelastic collision, a part of the initial kinetic energy of the system always changes into some other form of energy.

25. In which of the following the momentum and energy of each body not conserved?
a) Inelastic collision
b) Oblique collision
c) Elastic collision
d) Head on collision

Answer: c
Explanation: Inelastic collision, total momentum and total energy of the entire system are conserved and not individual bodies.

26. In an elastic collision of two billiard balls, the total kinetic energy is conserved ___________
a) Completely
b) For a short duration
c) For a long duration but not completely
d) Never

Answer: b
Explanation: During the short time of collision when the balls are in contact, the kinetic energy of the balls gets converted into the potential energy. In an elastic collision, though the kinetic energy before the collision is equal to the kinetic energy after the collision but kinetic energy is not conserved during the short time of collision.

27. Which of the following is an example for a force which does work on a body but fails to change its kinetic energy?
a) A body pulled through a plain surface
b) A body pulled through a vertical surface
c) A body pulled through a horizontal surface
d) A body at rest

Answer: c
Explanation: When a body is pulled through a rough horizontal surface with constant velocity, work is done by the applied force on the body but the kinetic energy of the body remains unchanged.

28. The mechanical energy of a system is always conserved.
a) True
b) False

Answer: b
Explanation: The mechanical energy is conserved only when conservative forces are involved and the system should be isolated. Thus the mechanical energy is not always conserved.

29. Two masses of 1g and 4g are moving with equal kinetic energy. The ratio of the magnitudes of their momenta is ___________
a) 4:1
b) √2:1
c) 1:2
d) 1:16

Answer: c
Explanation: p = √2mK
For same K, P1P2=m1m2−−−√=12 = 1:2.

30. If a machine is lubricated with oil ___________
a) The mechanical advantage of the machine increases
b) The mechanical efficiency of the machine increases
c) Both its mechanical advantage and efficiency increases
d) Its efficiency increases, but its mechanical advantage decreases

Answer: b
Explanation: When a machine is lubricated with oil, energy wastage against friction decreases. This increases the mechanical efficiency of the machine.

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31.The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is
Moderately small
Extremely large
Extremely small
Depends on a particular case
Answer: (b) Extremely small

32. In an elastic collision of two particles the following is conserved
Speed of each particle
Kinetic energy of each particle
Total kinetic energy of both the particles
Momentum of each particle
Answer: (c) Total kinetic energy of both the particles

33. A shell initially at rest explodes into two pieces of equal mass, then the two pieces will
Move with different velocities in different directions
Be at rest
Move with the same velocity in the same direction
Move with the same velocity in opposite directions
Answer: (d) Move with the same velocity in opposite directions

34.A lead ball strikes a wall and falls down, a tennis ball having the same mass and velocity strikes the wall and bounces back. Check the correct statement.
The lead ball suffers a greater change in momentum compared with the tennis ball
The tennis ball suffers a greater change in momentum as compared with the lead ball
The momentum of the lead ball is greater than that of the tennis ball
Both suffer an equal change in momentum
Answer: (b) The tennis ball suffers a greater change in momentum as compared with the lead ball

35.When two bodies collide elastically, then
Kinetic energy of the system alone is conserved
Only momentum is conserved
Both energy and momentum are conserved
Neither energy nor momentum is conserved
Answer: (c) Both energy and momentum are conserved

36.The coefficient of restitution for a perfectly elastic collision is
1
0
∞
-1
Answer: (a) 1

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37. Two balls at same temperature collide. What is conserved?
Temperature
Kinetic energy
Momentum
Velocity
Answer: (c) Momentum

38.A body of mass M collides against a wall with a velocity V and retraces its path with the same speed. The change in momentum is (take the initial direction of the velocity as positive)
2 Mv
1 Mv
-2 Mv
Zero
Answer: (c) -2 Mv

39.A shell of mass m moving with velocity v suddenly breaks into 2 pieces. The part having mass m/4 remains stationary. The velocity of the shell will be
(4/3)v
V
2 v
¾ v
Answer: (a) (4/3)v

40. A metal ball falls from a height of 32 metres on a steel plate. If the coefficient of restriction is 0.5 to what height will the ball rise after the second bounce
4 m
8 m
2 m
16 m
Answer:(c) 2 m

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41. A bullet of 5 gms travels with a velocity of 100 m/sec. It penetrates a wooden block up to 6 cm. What is the average force imposed on the block by the bullet?
0
417 N
830 N
830 N
Answer: (b) 417 N

42. The second law of motion gives the measure of which of the following?
Force
Acceleration
Momentum
Angular Momentum
Answer: (a) Force

43. What is the velocity of a body of mass 5 gm if a force of 100 dynes acts on the body for 10 seconds?
2000 cm/sec
200 cm/sec
20 cm/sec
2 cm/sec
Answer: (b) 200 cm/sec

44. An object will possess uniform motion as long as the
resultant force acting on it begins to decrease
resultant force on acting on it increases continuously
resultant force is right angles to its rotation
resultant force acting on it is zero
Answer: (d) resultant force acting on it is zero

45. What is the accelerating force on the Diwali rocket if it ejects 0.05 kg of gases per second at a velocity fo 400 m/s?
20 N
20 dynes
1000 N
22 dynes
Answer: (a) 20 N

46. A coin dropped in the lift takes time t1 to reach the floor when the lift is stationary and time t2 when the lift moves with a constant acceleration. Which of the following relation is true?
t₁>t₂
t₂>t₁
t₁=t₂
t₁>>t₂
Answer: (a) t₁>t₂

47. A person standing in the elevator finds his weight to be lesser than his actual weight in which of the following cases?
When the elevator moves upward with constant acceleration
When the elevator moves downward with constant acceleration
When the elevator moves upward with constant velocity
When the elevator moves downward with constant velocity
Answer: (b) When the elevator moves downward with constant acceleration

48. A parachutist weighing w strikes the ground with his legs fixed and comes to rest with an upward acceleration of 3 g. What is the force exerted by him during landing?
w
2w
3w
4w
Answer: (d) 4w

49. A man stands on a weighing machine in the lift. When the lift is stationary his weight is recorded as 40 kg. If the lift accelerates upwards with an acceleration of 2 m/s² what weight will the machine show?
40 kg
48 kg
42 kg
32 kg
Answer: (b) 48 kg

50. Two trolleys of mass m and 3m are connected by a string. When they are compressed and released, they move off in opposite directions and come to rest after covering a distance of S1 and S2 respectively. Assuming the coefficient of friction to be constant, the ratio of S1: S2 is
1:9
1:3
3:1
9:1
Answer: (d) 9:1

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52.What will happen if the body at rest is made to move in a straight line and obstructed by an opposite force?
The body slows down
The body changes direction
The body will continue to move in the same direction at the same speed
All of the above
Answer: (a) The body slows down

53. What is the apparent weight of the body travelling upwards with an acceleration of 2 m/s² and has a mass of 10 kg?
198 N
140 N
118 N
164 N
Answer: (c) 118 N

54. On a body of 20 kg, a force of 10 N acts for 10 seconds. What is the change in its momentum?
1000 kg.m/s
200 kg.m/s
100 kg.m/s
5 kg.m/s
Answer: (c) 100 kg.m/s

55. A machine gun fires a bullet of mass 40 g with a velocity of 1200 ms^-1. The man holding it cam exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
One
Two
Three
Four
Answer: (c) Three

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57. Internal force is responsible for the change in velocity of an object.
a) True
b) False

Answer: b
Explanation: The outside force exerted on an object by an external agency is called an external force. Such a force changes the velocity of an object.

58. Internal force holds together the particles as a single object.
a) True
b) False

Answer: a
Explanation: The mutual forces exerted by the particles of a system on one another are called internal forces. These forces are responsible for holding together the particles as a single object.

59. A hammer is resting on a plane surface. If force P is applied on the hammer along with a line not passing through its centre of mass, them the hammer _____________
a) Moves along a straight line path
b) Stays still
c) Is thrown away
d) Rotates about its centre of mass

Answer: d
Explanation: If a single force acts on a body and the line of action of force passes through the centre of mass, the body will have only linear acceleration. When the force is applied along with a line not passing through its centre of mass, then the hammer rotates about its centre of mass.

60. The point where whole weight may be assumed to act is called ___________
a) Centre of mass
b) Centre of weight
c) Centre of gravity
d) Centre of acceleration

Answer: c
Explanation: The centre of mass of a body is the point where the whole mass of the body may be assumed to be concentrated for describing its translator motion. On the other hand, the centre of gravity is a point at which the resultant of gravitational forces on all particles of the body acts.

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61. The Sun’s attraction of both earth and moon are external forces acting on the centre of mass of the earth-moon system.
a) True
b) False

Answer: a
Explanation: The moon moves around the earth in a circular orbit and the earth moves around the sun in an elliptical orbit. Here the mutual force of gravitation between the earth and the moon are internal forces while the Sun’s attraction of both earth and moon are the external forces acting on the centre of mass of the earth-moon system.

62. Which of the following retain their relative positions even when they move under the action of an external force?
a) Rotation body
b) Stationary body
c) Rigid body
d) A body in equilibrium

Answer: c
Explanation: A body is said to be rigid if it does not undergo any change in its size and shape, however large the external force may be acting on it. A rigid body is one whose constituent particles retain their relative positions even when they move under the action of an external force.

63. On the application of constant torque, a wheel is turned from rest through 400 radians in 10s. Find the angular acceleration.
a) 6 rad/s²
b) 4 rad/s²
c) 2 rad/s²
d) 8 rad/s²

Answer: d
Explanation: θ=400rad
ω_0=0, t = 10s, α = ?
θ=ω₀ t+1/2 αt²
400 = 0+1/2 α10²
α = 8 rad/s².

64. A ball of mass 2kg and another of mass 4kg are dropped together from a 60feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ration of ___________
a) √2:1
b) 1:4
c) 1:2
d) 1:√2

Answer: c
Explanation: Both balls attain the same velocity v after falling through 30 feet height.
E₁/E₂ = (1/2 m₁ (v₁)²)/(1/2 m₂ (v₂)²) = (2v²)/(4v²)=1/2=1:2.

65. How much water a pump of 2kW can raise in one minute to a height of 10m? (g=10m/s²)
a) 1000litres
b) 1200litres
c) 10litres
d) 2000litres

Answer: b
Explanation: P = W/t=mgh/t
m = Pt/gh=(2000×60)/(10×10)=1200kg.

66. A body of mass of 2kg is placed on a rough horizontal plane. The coefficient of friction between body and the plane is 0.2. Then ___________
a) Body will move in forwarding direction if F=3N
b) Body will move in a backward direction with the acceleration of 0.5m/s², if force F=3N
c) If F=3N, then the body will be in rest condition
d) The body will move both forward during a particular period and then remain at rest

Answer: d
Explanation: Limiting friction, f = μR = μmg = 0.2×2×9.8=3.92N
When F>3.92N the body will move in a forward direction. When F=3N, the body will move to remain at rest.

67.A block is displaced by 3 m when a force of 200 N is applied on it on an inclined surface which is at an angle of 50^o with the horizontal. What is the work done?
a. 385.67 Nm
b. 459.62 Nm
c. 933.00 Nm
d. Insufficient data

ANSWER: 385.67 Nm

68. Which of the following is represented by the area under the force-displacement diagram?
a. Impulse
b. Momentum
c. Power
d. Work done

ANSWER: Work done

69.According to work-energy principle, a particle of mass m when subjected to an unbalanced force system, the work done during displacement by all forces is equal to change in ____________ during displacement.
a. gravitational energy
b. kinetic energy
c. mechanical energy
d. potential energy

ANSWER: kinetic energy

70.The force for which work done is independent of _______ is called as conservative force
a. distance
b. path
c. time
d. all of the above

ANSWER: path

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71. Which of the following factors are related to the work-energy principle?
a. force, displacement and time
b. force, velocity, time and mass
c. force, velocity, displacement
d. displacement, time and mass

ANSWER: force, velocity, displacement

72.What is the S.I unit of work done?
a. Joule
b. Newton meter
c. Both a. and b.
d. None of the above

ANSWER: Both a. and b.

73.Work done by an engine in 6 sec is 1000 joules. What is the power generated by the engine in watt?
a. 1600 watt
b. 600 watt
c. 166 watt
d. 600 watt

ANSWER: 166 watt

74.According to the principle of conservation of energy, under the action of _________ force, the sum of P.E and K.E of a particle remains constant.
a. conservative force
b. dissipative force
c. frictional force
d. air resistance force

ANSWER: conservative force

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