Question

Trolley, X moving along a horizontal frictionless track, collides with a stationary trolley Y. The two trolleys become attached and move off together. Which statement about this interaction is correct?
A. Some of the kinetic energy of trolley X is changed to momentum in the collision
B. Some of the momentum of trolley X is changed to kinetic energy in the collision
C. Trolley X loses some of its momentum as heat in the collision
D. Trolley X shares its momentum with trolley Y but some of its kinetic energy is lost

Answer 1

Hint: To answer the following question we need to first determine the kind of collision that has been mentioned in the question. After we have examined the kind of collision, we need to compare all the statements that are mentioned as options. This will help us to find the correct answer.

Complete step by step answer:
 The situation that has been mentioned in the question, is an example of inelastic collision. The above question can be displayed as:

By inelastic collision, we mean a collision in which the kinetic energy is not conserved. This is because there is the action of the internal friction that comes into action. However, we should also know that the momentum of the body is conserved in case of inelastic collision.
So, as the situation mentioned in the question is an inelastic collision, we can conclude the following:
1. Momentum will be conserved.
2. Some part of the kinetic energy will be lost due to the deformation of the bodies that are colliding.
In option A, it is clearly mentioned that kinetic energy changes into momentum, which is false. So this statement is incorrect.
In option B, it is clearly mentioned that the momentum of the body is changed to kinetic energy. This does not fulfil the criteria of inelastic collision. So, this statement is incorrect.
In option C, it is mentioned that momentum is lost, which again is not true for the inelastic collision. So, the statement is not true.
In option D, it is mentioned that some of the momentum of X is shared by Y. This signifies that the momentum is not lost. And it is also mentioned that kinetic energy is lost. So, this statement is true.
Therefore, the correct answer is Option D.
Note: We should know that the total energy of the system is always conserved. But the kinetic energy which is carried by the moving objects, that are taken into consideration, is not always conserved. In the case of inelastic collision, energy is lost to the environment and is transferred in various other forms. One such way of transfer of energy can be heat.