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WORK AND ENERGY:-- OBJECTIVE-II
1. A heavy stone is thrown from a cliff of height h in a given direction. The speed with which it hits the ground
(a) must depend on the speed of projection
(b) must be larger than the speed of projection
(c) must be independent of the speed of projection
(d) may be smaller than the speed of projection.
Answer:- (a), (b)
2. The total work done on a particle is equal to the change in its kinetic energy
(a) always
(b) only if the forces acting on it are conservative
(c) only if gravitational force alone acts on it
(d) only if elastic force alone acts on it.
Answer:- (a)
Explanation: Whatever be the force, the work done on the particle by the resultant force is always equal to the change in its K.E. (Either increase or decrease).
3. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that
(a) its velocity is constant
(b) its acceleration is constant
(c) its kinetic energy is constant
(d) it moves in a circular path
Answer:- (c), (d)
4. Consider two observers moving with respect to each other at a speed v along a straight line. They observe a block of mass m moving a distance l on a rough surface. The following quantities will be same as observed by the two observers
(a) kinetic energy of the block at time t
(b) work done by friction
(c) total work done on the block
(d) acceleration of the block.
Answer:- (d)
Explanation: Since the observers are moving with respect to each other at a speed v, they will find the block moving at different speeds. Kinetic energy observed by each one will be different at any time t. So the answer is not (a).
Since the direction of movement of the block is not given, each observer may see it moving a different distance. So they may observe different work done by friction.
Total work done on the block will be equal to change in K.E. But the velocities observed by both the observers are different. So for them change in K.E. will be different. Answer (c) is not correct.
Acceleration is the rate of change of velocity. Though for both observers velocities are different but the difference of velocities are same, means the rate of change of velocities (acceleration) is same. So the answer is (d).
5. You lift a suitcase from the floor and keep it on a table. The work done by you on the suitcase does not depend on
(a) the path taken by the suitcase
(b) the time taken by you in doing so
(c) the weight of the suitcase
(d) your weight.
Answer:- (a), (b), (d).
Explanation: Since the force applied by me is a conservative force, the work done by me on the suitcase does not depend on the path taken by the suitcase. (a).
Work done is the product of force and displacement. It does not depend on time. (b).
It does not depend on my weight because we are calculating work done by me on the suitcase. (d).
But it depends on the weight of the suitcase. So (c) is not correct.
6. No work is done by a force on an object if
(a) the force is always perpendicular to its velocity
(b) the force is always perpendicular to its acceleration
(c) the object is stationary but the point of application of the force moves on the object
(d) the object moves in such a way that the point of application of the force remains fixed.
Answer:- (a), (c), (d).
Explanation: Since there is no displacement along the force when it is perpendicular to the velocity of an object, so no work is done. Answer (a).
1. A heavy stone is thrown from a cliff of height h in a given direction. The speed with which it hits the ground
(a) must depend on the speed of projection
(b) must be larger than the speed of projection
(c) must be independent of the speed of projection
(d) may be smaller than the speed of projection.
Answer:- (a), (b)
Explanation: Since Kinetic Energy given to the stone is dependent on the speed of projection, and the speed with which it hits the ground is dependent upon the K.E. given to the stone at the time of projection, Hence answer (a).
When the stone hits the ground its K.E. is the sum of K.E. given to it at the time of projection and the Potential energy at the point of projection with respect to the ground. That means K.E. of the stone is more at the ground than the point of projection. Since K.E. of a given mass particle is only dependent on its speed, so its speed when it hits the ground must be larger than the speed of projection. Hence (b).
(c) and (d) are opposite to the above condition, hence not true.
(c) and (d) are opposite to the above condition, hence not true.
(a) always
(b) only if the forces acting on it are conservative
(c) only if gravitational force alone acts on it
(d) only if elastic force alone acts on it.
Answer:- (a)
Explanation: Whatever be the force, the work done on the particle by the resultant force is always equal to the change in its K.E. (Either increase or decrease).
3. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that
(a) its velocity is constant
(b) its acceleration is constant
(c) its kinetic energy is constant
(d) it moves in a circular path
Answer:- (c), (d)
Explanation: Since the force is always perpendicular to the velocity, it means there is no displacement in the direction of force i.e. no work is done on the particle. Hence no change in the Kinetic Energy, so K.E. is constant. Hence answer (c).
Since the particle is acted upon by a force, its velocity must change according to Newtons Second Law of Motion and this change must be in the direction of the force. Since the force is always perpendicular to the velocity it only changes its direction, not the magnitude. It results in movement of the particle in a circular path in which the force is always along the radius. Hence answer (d), not (a).
Again the acceleration is in the radial direction (i.e. in the direction of force) and in the circular motion, this direction of acceleration always changes because the direction of force changes constantly. So (b) is not correct.
4. Consider two observers moving with respect to each other at a speed v along a straight line. They observe a block of mass m moving a distance l on a rough surface. The following quantities will be same as observed by the two observers
(a) kinetic energy of the block at time t
(b) work done by friction
(c) total work done on the block
(d) acceleration of the block.
Answer:- (d)
Explanation: Since the observers are moving with respect to each other at a speed v, they will find the block moving at different speeds. Kinetic energy observed by each one will be different at any time t. So the answer is not (a).
Since the direction of movement of the block is not given, each observer may see it moving a different distance. So they may observe different work done by friction.
Total work done on the block will be equal to change in K.E. But the velocities observed by both the observers are different. So for them change in K.E. will be different. Answer (c) is not correct.
Acceleration is the rate of change of velocity. Though for both observers velocities are different but the difference of velocities are same, means the rate of change of velocities (acceleration) is same. So the answer is (d).
5. You lift a suitcase from the floor and keep it on a table. The work done by you on the suitcase does not depend on
(a) the path taken by the suitcase
(b) the time taken by you in doing so
(c) the weight of the suitcase
(d) your weight.
Answer:- (a), (b), (d).
Explanation: Since the force applied by me is a conservative force, the work done by me on the suitcase does not depend on the path taken by the suitcase. (a).
Work done is the product of force and displacement. It does not depend on time. (b).
It does not depend on my weight because we are calculating work done by me on the suitcase. (d).
But it depends on the weight of the suitcase. So (c) is not correct.
6. No work is done by a force on an object if
(a) the force is always perpendicular to its velocity
(b) the force is always perpendicular to its acceleration
(c) the object is stationary but the point of application of the force moves on the object
(d) the object moves in such a way that the point of application of the force remains fixed.
Answer:- (a), (c), (d).
Explanation: Since there is no displacement along the force when it is perpendicular to the velocity of an object, so no work is done. Answer (a).
(b) is not true because the acceleration will always be in the direction of force according to Newton's Second Law of Motion.
No work is done if there is no displacement of the object in the direction of the force. Answer (c).
Again there is no displacement along the force, no work done. Answer (d).
7. A particle of mass m is attached to a light string of length l, the other end of which is fixed. Initially, the string is kept horizontal and the particle is given an upward velocity v. The particle is just able to complete a circle.
(a) The string becomes slack when the particle reaches its highest point.
(b) The velocity of the particle becomes zero at the highest point.
(c) The kinetic energy of the ball in initial position was ½mv²=mgl.
(d) The particle again passes through the initial position.
Answer:- (a), (d).
Explanation: Since the particle is just able to complete the circle, at the highest point only its weight keeps it in circular path and tension in the string will be zero, Answer (a).
(b) is not true because as given the particle completes a circle. At the highest point, it must have horizontal velocity =√(gl).
(c) is not true because initial K.E. should be equal to ½mv² =mgl+½mgl.
(d)Since no further work is done on the particle by an external force, the total mechanical energy of the system remains constant and the particle passes the initial position with same initial velocity.
8. The kinetic energy of a particle continuously increases with time.
(a) The resultant force on the particle must be parallel to the velocity at all instants.
(b) The resultant force on the particle must be at an angle less than 90° all the time.
(c) Its height above the ground level must continuously decrease.
(d) The magnitude of its linear momentum is increasing continuously.
Answer:- (b), (d).
Explanation: Since K.E. of the particle continuously increases, means its velocity continuously increases i.e. it is accelerated. It can only happen if there is a positive component of the resultant force (F.cosθ) along the velocity. For it to happen the resultant force on the particle must be at an angle less than 90° all the time. Hence option (b).
(a) is not true because it is only a special case of the condition in (b) when the angle θ=0° and it need not be a necessary condition.
(c) is not true because the direction of the velocity is not given.
(d) is true because the magnitude of v increases continuously hence the magnitude of linear momentum mv also increases continuously.
9. One end of a light spring of spring constant 'k' is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is ½kx². The possible cases are
(a) The spring was initially compressed by a distance 'x' and was finally in its natural length.
(b) It was initially stretched by a distance 'x' and finally was in its natural length.
(c) It was initially in its natural length and finally in a compressed position.
(d) It was initially in its natural length and finally in a stretched position.
Answer:- (a), (b).
Explanation: Since in the conditions of (c) and (d) spring does not exert a force that is in the direction of displacement but in the opposite, so the work done will be negative.
Only in (a) and (b) the work done will be positive.
10. A block of mass M is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force F. The kinetic energy of the block increases by 20 J in 1 s.
(a) The tension in the string is Mg.
(b) The tension in the string is F.
(c) The work done by the tension on the block is 20 J in the above 1 s.
(d) The work done by the force of gravity is -20 J in the above 1 s.
Answer:- (b)
Explanation: (a) is not true because if the tension in the string is Mg the block cant be pulled up. It can only happen when the tension in the string is F. So (b) is true.
Since K.E. of the block increases by 20J, it means work done by the resultant force on the block is 20 J. But neither the tension nor the force of gravity is the resultant force on the block. Hence (c) and (d) are not true.
7. A particle of mass m is attached to a light string of length l, the other end of which is fixed. Initially, the string is kept horizontal and the particle is given an upward velocity v. The particle is just able to complete a circle.
(a) The string becomes slack when the particle reaches its highest point.
(b) The velocity of the particle becomes zero at the highest point.
(c) The kinetic energy of the ball in initial position was ½mv²=mgl.
(d) The particle again passes through the initial position.
Answer:- (a), (d).
Explanation: Since the particle is just able to complete the circle, at the highest point only its weight keeps it in circular path and tension in the string will be zero, Answer (a).
(b) is not true because as given the particle completes a circle. At the highest point, it must have horizontal velocity =√(gl).
(c) is not true because initial K.E. should be equal to ½mv² =mgl+½mgl.
(d)Since no further work is done on the particle by an external force, the total mechanical energy of the system remains constant and the particle passes the initial position with same initial velocity.
8. The kinetic energy of a particle continuously increases with time.
(a) The resultant force on the particle must be parallel to the velocity at all instants.
(b) The resultant force on the particle must be at an angle less than 90° all the time.
(c) Its height above the ground level must continuously decrease.
(d) The magnitude of its linear momentum is increasing continuously.
Answer:- (b), (d).
Explanation: Since K.E. of the particle continuously increases, means its velocity continuously increases i.e. it is accelerated. It can only happen if there is a positive component of the resultant force (F.cosθ) along the velocity. For it to happen the resultant force on the particle must be at an angle less than 90° all the time. Hence option (b).
(a) is not true because it is only a special case of the condition in (b) when the angle θ=0° and it need not be a necessary condition.
(c) is not true because the direction of the velocity is not given.
(d) is true because the magnitude of v increases continuously hence the magnitude of linear momentum mv also increases continuously.
9. One end of a light spring of spring constant 'k' is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is ½kx². The possible cases are
(a) The spring was initially compressed by a distance 'x' and was finally in its natural length.
(b) It was initially stretched by a distance 'x' and finally was in its natural length.
(c) It was initially in its natural length and finally in a compressed position.
(d) It was initially in its natural length and finally in a stretched position.
Answer:- (a), (b).
Explanation: Since in the conditions of (c) and (d) spring does not exert a force that is in the direction of displacement but in the opposite, so the work done will be negative.
Only in (a) and (b) the work done will be positive.
10. A block of mass M is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force F. The kinetic energy of the block increases by 20 J in 1 s.
(a) The tension in the string is Mg.
(b) The tension in the string is F.
(c) The work done by the tension on the block is 20 J in the above 1 s.
(d) The work done by the force of gravity is -20 J in the above 1 s.
Answer:- (b)
Explanation: (a) is not true because if the tension in the string is Mg the block cant be pulled up. It can only happen when the tension in the string is F. So (b) is true.
Since K.E. of the block increases by 20J, it means work done by the resultant force on the block is 20 J. But neither the tension nor the force of gravity is the resultant force on the block. Hence (c) and (d) are not true.
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Links to the chapter -
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CHAPTER- 10 - Rotational Mechanics
Questions for Short Answers
OBJECTIVE - I
OBJECTIVE - II
EXERCISES - Q-1 TO Q-15
EXERCISES - Q-16 TO Q-30
CHAPTER- 10 - Rotational Mechanics
Questions for Short Answers
OBJECTIVE - I
OBJECTIVE - II
EXERCISES - Q-1 TO Q-15
EXERCISES - Q-16 TO Q-30
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
HC Verma's Concepts of Physics, Chapter-8, WORK AND ENERGY
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HC Verma's Concepts of Physics, Chapter-7, Circular Motion
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HC Verma's Concepts of Physics, Chapter-6, Friction
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For more practice on problems on friction solve these "New Questions on Friction" .
Click here for → Friction - OBJECTIVE-II
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Click here for → Exercises (11-20)
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For more practice on problems on friction solve these "New Questions on Friction" .
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HC Verma's Concepts of Physics, Chapter-5, Newton's Law's of Motion
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Click here for→ Newton's laws of motion - Objective - I
Click here for → Newton's Laws of Motion - Objective -II
Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)
Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)
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HC Verma's Concepts of Physics, Chapter-4, The Forces
"Questions for short Answers"
Click here for "The Forces" - OBJECTIVE-I
Click here for "The Forces" - OBJECTIVE-II
Click here for "The Forces" - Exercises
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