Question

A block of mass $m$ moving at a velocity $v$ collides head on with another block of mass $2m$ at rest. If the coefficient of restitution is $\frac{1}{2}$, find the velocities of the blocks after the collision.

• A. $\frac{V}{2},\frac{V}{2}$
• B. $\frac{V}{2},\frac{-V}{2}$
• C. $\frac{V}{2},0$
• D. $0,\frac{V}{2}$

Answer 1

The correct option is D

$0,\frac{V}{2}$

Suppose after the collision the block of mass $m$ moves at a velocity $u_1$ and the block of mass $2m$ moves at a velocity $u_2$. By conservation of momentum,

$mv$ = $m{u}_1+2m{u}_2$ ..........(i)

the velocity of separation is $u_2-u_1$ and the velocity of approach is $-v$.

so, $u_2-u_1$ = $-\frac{1}{2}\times (-v)$ ...........(ii)

from (i) and (ii), $u_1$ = 0 and $u_2$ = $\frac{v}{2}$