Question

prove that coefficient of restitution of a perfectly elastic collision in one dimension is unity.​

Answer 1

Let there be two bodies of mass M and m, let the body M be moving with velocity V and the body m be at rest. 

Now when the body (M) will collide with the body (m) the KE would be conserved hence the body M will come to rest and body m will move with velocity V.

Putting the value of variables in the equation below;

e=v-u/u-v

 where V is velocity of separation of body M ,

           v is velocity of separation of body m,

           U is velocity of approach of body M,

           u is velocity of approach of body m.

⇒ e= 0-v/u-0

since, v=U

⇒ e=1

Hence Proved

Answer 2

coefficient of restitution (e) value depends on nature of the material of colliding bodies so

e=1 for elastic collision