Question

Two balls of mass $3\text{kg}$ and $6\text{kg}$ are moving towards each other with velocities $6\text{m/s}$ and $3\text{m/s}$ respectively on a frictionless surface. After colliding, the $3\text{kg}$ ball returns with velocity $3\text{m/s}$. Velocity of $6\text{kg}$ ball (after collision) and coefficient of restitution are respectively:

• A. $1.5\text{m/s},0.5$
• B. $2\text{m/s},0.20$
• C. $3\text{m/s},1$
• D. $2.2\text{m/s},0.3$

Answer 1

The correct option is A $1.5\text{m/s},0.5$


If $u_1=6\text{m/s},u_2=-3\text{m/s}$
(taking rightward +ve)
After collision, velocity of $3\text{kg}$ ball $=v_1=-3\text{m/s}$
Let velocity of $6\text{kg}$ ball $=v_2\left(say\right)$

Applying linear momentum conservation,
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$\Rightarrow 3\times 6+6\times (-3)=3\times (-3)+6v_2$
$\Rightarrow 0=-9+6v_2$
$\Rightarrow v_2=\frac{9}{6}=\frac{3}{2}=1.5\text{m/s}$
and $e=\frac{V_{separation}}{V_{approach}}=\frac{-3-1.5}{-3-6}=\frac{1}{2}$