Question

Two balls of masses $3\text{kg}$ and $5\text{kg}$ are moving towards each other with speeds $5\text{m/s}$ and $3\text{m/s}$ respectively on a frictionless surface as shown in figure. After collision, the $5\text{kg}$ ball retraces its path with speed $2\text{m/s}$. Find the coefficient of restitution.

• A. $1$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{8}{3}$

Answer 1

The correct option is C $\frac{2}{3}$

Given,
$m_1=3\text{kg};m_2=5\text{kg}$
$u_1=5\text{m/s};u_2=-3\text{m/s}$, $v_2=2\text{m/s}$
Let velocity of $m_1$ after collision $v_1=-v\text{m/s}$
(taking rightward +ve)

Using $PCLM$,
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$3\left(5\right)+5(-3)=3(-v)+5\left(2\right)$
$\Rightarrow v=\frac{10}{3}\text{m/s}$

Therefore, cofficient of restitution
$e$ = $\frac{v_2-v_1}{u_1-u_2}=\frac{2+\frac{10}{3}}{5+3}=\frac{2}{3}$