NCERT Class 11 Physics Solutions: Chapter 6 – Work, Energy, and Power Part 4

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Question 6.6:

Underline the correct alternative:

(a) When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered.

(b) Work done by a body against friction always results in a loss of its kinetic/potential energy.

(c) The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system.

(d) In an inelastic collision of two bodies, the quantities, which do not change after the collision, are the total kinetic energy/total linear momentum/total energy of the system of two bodies.

Answer:

(a) When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered

Correct alternative: Decreases

Explanation:

A conservative force does a positive work on a body when it displaces the body in the direction of force. As a result, the body advances toward the centre of force. It decreases the separation between the two, thereby decreasing the potential energy of the body.

(b) Work done by a body against friction always results in a loss of its kinetic/potential energy,

Correct alternative: Kinetic energy

Explanation:

The work done against the direction of friction reduces the velocity of a body. Hence, there is a loss of kinetic energy of the body.

(c) The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system,

Correct alternative: External force

Explanation:

Internal forces, irrespective of their direction, cannot produce any change in the total momentum of a body. Hence, the total momentum of a many-particle system is proportional to the external forces acting on the system.

(d) In an inelastic collision of two bodies, the quantities, which do not change after the collision, are the total kinetic energy/total linear momentum/total energy of the system of two bodies,

Correct alternative: Total linear momentum

Explanation:

The total linear momentum always remains conserved whether it is an elastic collision or an inelastic collision.

Question 6.7:

State if each of the following statements is true or false. Give reasons for your answer.

(a) In an elastic collision of two bodies, the momentum and energy of each body is conserved.

(b) Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

(c) Work done in the motion of a body over a closed loop is zero for every force in nature.

(d) In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Answer:

(a) In an elastic collision of two bodies, the momentum and energy of each body is conserved:

Ans: False

Explanation:

In an elastic collision, the total energy and momentum of both the bodies, and not of each individual body, is conserved.

(b) Total energy of a system is always conserved, no matter what internal and external forces on the body are present:

Ans: False

Explanation:

Although internal forces are balanced, they cause no work to be done on a body. It is the external forces that have the ability to do work. Hence, external forces are able to change the energy of a system.

(c) Work done in the motion of a body over a closed loop is zero for every force in nature,

Ans: False

Explanation:

The work done in the motion of a body over a closed loop is zero for a conservation force only.

(d) In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system,

Ans: True

Explanation:

In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system. This is because in such collisions, there is always a loss of energy in the form of heat, sound, etc.

Question 6.8:

Answer carefully, with reasons:

(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?

(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls?

(c) What are the answers to (a) and (b) for an inelastic collision?

(d) If the potential energy of two billiard balls depends only on the separation distance between their centers, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

Answer:

(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact):

Ans: No

Explanation:

In an elastic collision, the total initial kinetic energy of the balls will be equal to the total final kinetic energy of the balls. This kinetic energy is not conserved at the instant the two balls are in contact with each other. In fact, at the time of collision, the kinetic energy of the balls will get converted into potential energy.

(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls:

Ans: Yes

Explanation:

In an elastic collision, the total linear momentum of the system always remains conserved.

(c) What are the answers to (a) and (b) for an inelastic collision:

Ans: No, Yes

Explanation:

In an inelastic collision, there is always a loss of kinetic energy, i.e., the total kinetic energy of the billiard balls before collision will always be greater than that after collision. The total linear momentum of the system of billiards balls will remain conserved even in the case of an inelastic collision.

(d) If the potential energy of two billiard balls depends only on the separation distance between their centers, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy):

Ans: Elastic

Explanation:

In the given case, the forces involved are conservation. This is because they depend on the separation between the centers of the billiard balls. Hence, the collision is elastic.