Question

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

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

Answer 1

The correct option is A $0,1$

Here, $m_1=m,m_2=2m$
$u_1=2\text{m/s},u_2=0$
Coefficient of restitution, $e=0.5$
Let $v_1$ and $v_2$ be their respective velocities after collision.
Applying the law of conservation of linear momentum,
we get
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$\therefore m\times 2+2m\times 0=m\times v_1+2m\times v_2$
$\Rightarrow 2m=m{v}_1+2m{u}_2$
$\Rightarrow 2=(v_1+2v_2)$ ... (1)
By definition of coefficient of restitution,
$e=\frac{v_2-v_1}{u_1-u_2}$
$\Rightarrow e(u_1-u_2)=v_1-v_2$
$\Rightarrow 0.5(2-0)=v_2-v_1$
$\Rightarrow 1=v_2-v_1$ ... (2)
Solving Eqs. (1) and (2), we get
$v_1=0\text{m/s},v_2=1\text{m/s}$
Hence, the correct answer is option (a).