Which of the following statement is true concening the elastic collision of two object (It is given that no net external force acts on the system of two object and the do not exen force on each other exept during collision)

Options

A. No net work on any of the two objects since there is no external on the system of given two object
B. The net work done by the first object on the second is equal in the net work done by the second on the first
C. The net work done by the first object on the second is execity the opposite of the net work done by the second on the fist
D. No net work done on the system depends on the angle of colision

Answer

C

Explanation

For the elastic collision, total kinetic energy is constant
If we consider both the colliding bodies as system then net work done on the system is zero (By work energy theorem)
`K_(1) + K_(2) = K'_(1) + K'_(2)` (1)
`K` is kinetic energy of object before the collision and `K'` is kinetic energy of object after the collision.
In general masses of both the object are different, so speed of each object becomes different after collision
`K_(1) != K'_(1)` and `K_(2) != K'_(2)`
By work energy theorem
`W_(1) = K'_(2) = K'_(1) - K_(1)` (2)`
`W_(2) = K'_(2) = K'_(2) - K_(2)` (3)`
From `(1), (2)` and (3) `W_(1) != 0, W_(2) != 0`
`W_(1) + W_(2) = 0`
`W_(1) = - W_(2)`
i.e., the work done by the first object on the second object is exactly the opposite of the work done by the second object on the first object.