Question

Which of the following statements is true concerning the elastic collision of two objects? (It is given that no net external force acts on the system of two object; and the objects do not exert force on each other except during collision)

• A.
  No net work is done on any of the two objects, since there is no external force on the system of given two objects.
  
• B.
  The net work done on the system depends on the angle of collision.
  
• C.
  The net work done by the first object on the second is exactly the opposite of the net work done by the second on the first.
  
• D.
  The net work done by the first object on the second is equal to the net work done by the second on the first.
  

Answer 1

The correct option is C

The net work done by the first object on the second is exactly the opposite of the net work done by the second on the first.

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)
$K_1+K_2=K_1^{{}^{\prime }}+K_2^{{}^{\prime }}$
$K$ is kinetic energy of object before the collision and $K^{\prime }$ is kinetic energy of object after the collision.In general masses of both the objects are different, so speed of each object becomes different after collision
$K_1\ne K_1^{{}^{\prime }}\text{and}{K}_2\ne K_2^{{}^{\prime }}$
By work energy theorem,$W_1=K_1^{{}^{\prime }}-K_1$
$W_2=K_2^{{}^{\prime }}-K_2$
$W_1\ne 0,W_2\ne 0$
$W_1+W_2=0$
$W_1=-W2$
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.
Final answer: (c)