Question

In head-on collision between two particles $A$ and $B$ of same mass, $A$ is moving with momentum $15kgm/s$, $B$ is stationary. During the impact, $B$ gives impulse $10N-s$ to $A$. The coefficient of restitution is

• A. $\frac{1}{4}$
• B. $1$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{1}{3}$

Diagram

$mu+0=m{v}_1+m{v}_2$

$v_1+v_2=u$

$v_1-v_2=-e(u-0)$

$v_1-v_2=-eu$

Solving the above equations, we get

$v_2=\frac{(1+e)u}{2}$

$m{v}_2=\frac{(1+e)mu}{2}$

Impulse, $J=m{v}_2\Rightarrow 10=\frac{(1+e)\left(15\right)}{2}$

$e=\frac{1}{3}$
Final answer: (b)