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 $\frac{1}{2}$, the velocities of the blocks after the collision respectively are and .

• A. \N
• B. v/2
• C. -v/2
• D. v

Answer 1

Answer: (A), (B)

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

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