KKMishra's Tutorials: November 2017

Sunday, November 19, 2017

Solutions to Problems on "Work and Energy" - H C Verma's Concepts of Physics, Part-I, Chapter-8, - OBJECTIVE -I

My Channel on YouTube ---> SimplePhysics with KK

For links to

other chapters - See bottom of the page

WORK AND ENERGY:-- OBJECTIVE-I

1. A heavy stone is thrown from a cliff of height h with a speed v. The stone will hit the ground with maximum speed if it is thrown
(a) vertically downward
(b) vertically upward
(c) horizontally
(d) the speed does not depend on the initial direction

Answer:- (d)
Explanation:- When the stone is thrown its total mechanical energy
= K.E.+P.E.
= ½mv² + mgh ---------(i)
This energy is conserved and when near the ground its P.E. is also converted to K.E. because of h=0. suppose it hits the ground with speed v', its total energy = ½mv'² -----(ii)
equating (i) and (ii) we get,
½mv'²=½mv²+mgh
v'²=v²+2gh
Clearly v' depends only on the value of v whatever be the initial direction.

2. Two springs A and B (k_A = 2k_B) are stretched by applying forces of equal magnitudes at the four ends. If the energy stored in A is E, that in B is
(a) E/2
(b) 2E
(c) E
(d) E/4

Answer:- (b)
Explanation:- Since (k_A = 2k_B) it means for the same force x_B = 2x_A . So if energy stored in spring A = E = F.x_A
Energy stored in spring B = F.x_B =F.2x_A =2E

3. Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is
(a) ½kx²
(b) -½kx²
(c) ¼kx²
(d) -¼kx².

Answer:- (d)
Explanation:- The work done by the spring on both of the masses is equal to the potential energy stored in the spring. The potential energy stored in the spring = -½kx². Since the masses are pulled out symmetrically, the work done by the string on each mass
=½(-½kx²) =-¼kx². The negative sign is for the fact that displacement is opposite to the force.

4. The negative of the work done by the conservative internal forces on a system equals the change in
(a) total energy
(b) kinetic energy
(c) potential energy
(d) none of these

Answer:- (c)
Explanation:- The Potential energy of a system is due to its configuration. When conservative internal forces do work on the system, the potential energy changes to kinetic energy. So negative of work done by the conservative internal forces will be the change in potential energy.

5. The work done by the external forces on a system equals the change in
(a) total energy
(b) kinetic energy
(c) potential energy
(d) none of these

Answer:- (a)
Explanation:- External forces will either change KE or PE or both of a system. Since total mechanical energy (KE+PE) of a system is conserved when no external force acts, hence work done by external force will change total mechanical energy.

6. The work done by all the forces (external and internal) on a system equals the change in
(a) total energy
(b) kinetic energy
(c) potential energy
(d) none of these

Answer:- (b)
Explanation:- Though work done by external forces will change the total energy of the system, work done by the internal forces will increase kinetic energy only. So when both do work KE is sure to change.

7. ------------ of a two-particle system depends only on the separation between the two particles. The most appropriate choice for the blank space in the above sentence is
(a) kinetic energy
(b) total mechanical energy
(c) potential energy
(d) total energy

Answer:- (c)
Explanation:- The potential energy of a system is due to its configuration and separation depicts the configuration.

8. A small block of mass m is kept on a rough inclined surface of inclination θ fixed in an elevator. The elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block in time t will be
(a) zero
(b) mgvt cos ²θ

(d) mgvt sin 2θ

Answer:- (c)
Explanation:- In time t, vertical distance covered =vt
The vertical component of frictional force = F.sinθ
Work done by this component
= F.sinθ .vt
= µmg.cosθ .sinθ .vt
= (sinθ /cosθ) mgvt.cosθ.sinθ (Since µ=tanθ)
= mgvt.sin ²θ
See Figure below,

Figure for problem 8

9. A block of mass m slides down a smooth vertical circular track. During the motion, the block is in
(a) vertical equilibrium
(b) horizontal equilibrium
(c) radial equilibrium
(d) none of these

Answer:- (d)
Self Explanatory.

10. A particle is rotated in a vertical circle by connecting it to a string of length l and keeping the other end of the string fixed. The minimum speed of the particle when the string is horizontal for which the particle will complete the circle is
(a) √(gl)
(b) √(2gl)
(c) √(3gl)
(d) √(5gl)

Answer:- (c)
Explanation:- Let speed at the top = v, it is balanced by weight mg,
so, mv²/l=mg
→v²= gl
Now let the speed when string is horizontal = v'
Here total energy = ½mv'²=½mv²+mgl
v'²=v²+2gl = gl+2gl =3gl
v'= √(3gl)

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Links for the chapter -

ALL LINKS
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

Questions for Short Answers

Objective - I

Objective - II

EXERCISES Q-1 TO Q-10

EXERCISES Q-11TO Q-20

EXERCISES Q-21 TO Q-30

EXERCISES Q-31 TO Q-42

EXERCISES Q-43 TO Q-54

HC Verma's Concepts of Physics, Chapter-8, WORK AND ENERGY

Click here for → Question for Short Answers
Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → EXERCISES(1-10)

Click here for → EXERCISES(11-20)
Click here for → Exercises (21-30)

HC Verma's Concepts of Physics, Chapter-7, Circular Motion

Click here for → Questions for Short Answer
Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II

Click here for → EXERCISES (1-10)
Click here for → EXERCISES (11-20)
Click here for → EXERCISES (21-30)

HC Verma's Concepts of Physics, Chapter-6, Friction

Click here for → Friction OBJECTIVE-I
Click here for → Friction - OBJECTIVE-II

Click here for → Questions for Short Answer

Click here for → OBJECTIVE-I
Click here for → Friction - OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → Exercises (11-20)

Click here for → EXERCISES (21-31)
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

Click here for → QUESTIONS FOR SHORT ANSWER

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)

Click here for→Newton's Laws of Motion,Exercises(Q.No. 28 to 42)

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HC Verma's Concepts of Physics, Chapter-4, The Forces

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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HC Verma's Concepts of Physics, Chapter-3, Kinematics-Rest and Motion:---

Click here for "Questions for short Answers"

Click here for "OBJECTIVE-I"

Click here for EXERCISES (Question number 1 to 10)

Click here for EXERCISES (Question number 11 to 20)

Click here for EXERCISES (Question number 21 to 30)

Click here for EXERCISES (Question number 31 to 40)

Click here for EXERCISES (Question number 41 to 52)

===============================================

Chapter -2, "Vector related Problems"

Click here for "Questions for Short Answers"

Click here for "OBJECTIVE-I

Click here for "OBJECTIVE-II"

Click here for "Exercises"

Wednesday, November 15, 2017

Solutions to Problems on "Work and Energy" - H C Verma's Concepts of Physics, Part-I, Chapter-8, - QUESTIONS FOR SHORT ANSWER

My Channel on You Tube ---> SimplePhysics with KK

For links to

other chapters - See bottom of the page

WORK AND ENERGY:-- Questions for Short Answer

1. When you lift a box from the floor and put it on an almirah the potential energy of the box increases, but there is no change in its kinetic energy. Is it a violation of conservation of energy?

Answer:- System's energy is conserved when no external force is applied. Here external force has done work on the box to increase its potential energy. It is not a violation of conservation of energy.

2. A particle is released from the top of an incline of height h. Does the kinetic energy of the particle at the bottom of the incline depend on the angle of incline? Do you need any more information to answer this question in Yes or No?

Answer:- No. The kinetic energy of the particle at the bottom of the incline does not depend on the angle of incline. It remains the same as the potential energy mgh is converted to kinetic energy. 'h' remains the same whatever be the angle of incline.
No more information is needed to answer the question.

3. Can the work by kinetic friction on an object be positive? Zero?

Answer:- Generally work done by the kinetic friction on an object is negative because the displacement is always opposite the friction force. But in some cases can be positive or zero.
For example, suppose one block is kept over other and lower block starts to move with some acceleration in such a way that upper block slides over the lower block. In this case, kinetic friction on the upper block acts along the direction of motion of lower block. Though upper block slides, even then it moves in the direction of the lower block with lesser velocity. So work done by kinetic fiction is positive.
Now suppose A block is moving over the ground. Kinetic friction acts between the block and the ground. On the block, it is acting backwards but on the ground, it is acting forwards. But there is no movement along this forward kinetic friction force, so work is zero.

4. Can static friction do nonzero work on an object? If yes give an example? If no, give reason.

Answer:- In above example suppose the upper block does not slide over the lower block. Now if the lower block moves, it applies static friction force on the upper block and the upper block moves in the direction of this static friction force. So nonzero work is done.

5. Can normal force do a nonzero work on an object? If yes, give an example. If no, give reason.

Answer:- Yes. For example, when a person is moving up or down in an elevator, the normal force on the person does nonzero work.

6. Can kinetic energy of a system be increased without applying any external force on the system?

Answer:- Yes. Suppose two opposite charged particles are at rest at a separation of l. As soon as they are released the particles start to move towards each other under the force of attraction and their velocities start to increase. So the kinetic energy of the system of these two particles which was zero initially (since u = 0) begins to increase because their velocities are increasing (K.E.= ½mv²). No external force is applied to this system of two particles even then the kinetic energy increases.

7. Is work energy theorem valid in non-inertial frames?

Answer:- Since the dynamics of a body cannot be explained in a non-inertial frame with real forces only so work-energy theorem is not valid but if we consider pseudo forces then Newton's laws can be applied and non-inertial frame can be treated as an inertial frame and work-energy theorem is valid.

8. A heavy box is kept on a smooth inclined plane and is pushed up by a force F acting parallel to the plane. Does the work done by the force F as the box goes from A to B depend on how fast the box was moving at A and B? Does the work by the force of gravity depend on this?

Answer:- Forces acting on the box are force F, Normal force N and weight of the box mg. Work done by the individual force F does not depend on how fast the box was moving at A and B (velocities) neither the work done by the individual force of gravity (mg). Only the work done by the resultant force on the box depends on the velocities at A and B (equal to the change in kinetic energy of the box).

9. One person says that the potential energy of a particular book kept in an almirah is 20 J and the other says it is 30 J. Is one of them necessarily wrong?

Answer:- No. One is free to choose the zero potential energy configuration as the origin is chosen arbitrarily. Hence the potential energy depends on this chosen configuration.

10. A book is lifted from the floor and is kept in an almirah. One person says that the potential energy of the book is increased by 20 J and the other says it is increased by 30 J. Is one of them necessarily wrong?

Answer:- Yes. Because in this case difference in potential energy depends on the height of the almirah which is fixed. So only one person is right and the other is necessarily wrong.

11. In one of the exercises to strengthen the wrist and fingers, a person squeezes and releases a soft rubber ball. Is the work done on the ball positive, negative or zero during compression? During expansion?

Answer:- Since the movement is along the force during compression the work done is positive. During expansion movement is opposite so the work done on the ball is negative.

12. In a tug of war, the team that exerts a larger tangential force on the ground wins. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. List which of the following works are positive, which are negative and which are zero?
(a) work by the winning team on the losing team
(b) work by the losing team on the winning team
(c) work by the ground on the winning team
(d) work by the ground on the losing team
(e) total external work done on the two teams.

Answer:-
(a) Positive
(b) Negative
(c) Zero (Assuming that work by ground means work by frictional force by ground, Also assuming the winning team does not step backwards)
(d) Negative (Assuming that work by ground means work by frictional force by ground, Losing team is dragged)
(e) Zero (Taking rope, both teams and ground as a system, no external force is on the system, so no external work done)

13. When an apple falls from a tree what happens to its gravitational potential energy just as it reaches the ground? After it strikes the ground?

Answer:- Since mechanical energy is conserved when no external force is applied, in this case, the gravitational potential energy is converted to kinetic energy just as it reaches the ground. After it strikes the ground, a part of this energy is used to deform the apple and other is converted to sound and heat energy.

14. When you push your bicycle up on an incline the potential energy of the bicycle and yourself increases. Where does this energy come from?

Answer:- Chemical energy (converted from food) stored in our muscle is converted to mechanical energy that increases the P.E. of myself with the bicycle. The energy in the food is received from sunlight.

15. The magnetic force on a charged particle is always perpendicular to its velocity. Can the magnetic force change the velocity of the particle? Speed of the particle?

Answer:- Since the magnetic force on the particle is perpendicular to its velocity, it can not change the speed of the particle but it can change its direction. Due to change in the direction, the velocity changes.

16. A ball is given a speed v₀ on a rough horizontal surface. The ball travels through a distance l on the surface and stops. (a) what are the initial and final kinetic energies of the ball? (b) what is the work done by the kinetic friction?

Answer:- (a) Initial Kinetic energy = ½mv₀²

Final Kinetic Energy = 0

(b) Forces on the ball are weight, normal force and kinetic friction. Since weight and normal force are equal and opposite, the resultant force on the ball is equal to kinetic friction. Work done by the resultant force is equal to change in kinetic energy, so work done by kinetic friction = 0-½mv₀² = - ½mv₀²

17. Consider the situation of the previous question from a frame moving with a speed v₀ parallel to initial velocity of the block. (a) What are the initial and final kinetic energies? (b) what is the work done by the kinetic friction?

Answer:- (a) In this moving frame initial velocity becomes zero, so initial K.E. =0, Final velocity = -v₀ , So final K.E. = ½mv₀²
(b) work done by kinetic friction = ½mv₀²

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