Question

A ball moving with velocity $2{\text{ms}}^{-1}$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in ${\text{ms}}^{-1}$) after collision will be

• A. $0,1$
• B. $1,1$
• C. $1,0.5$
• D. $0,2$

Answer 1

The correct option is A $0,1$

When two bodies collide head-on,
Coefficient of restitution, $e=\frac{v_2-v_1}{u_1-u_2}$
From law of conservation of momentum
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
Put, $u_1=2{\text{ms}}^{-1},u_2=0,m_1=m$
and $m_2=2m,e=0.5$
Combining the above two equations:
$v_1=\left[\frac{m-m}{m+2m}\right]\times 2$
$\Rightarrow v_1=0$
$v_2=\left[\frac{1.5\times m}{3m}\right]\times 2$
$v_2=1{\text{ms}}^{-1}$