Question

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

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

Answer 1

Answer: (A)

Here, $m_1=w,m_2=2m$
$u_1=2m/s,u_2=0$
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
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$\therefore m\times 2+2m\times 0=m\times v_1+2m\times v_2$
or $2m=m{v}_1+2m{v}_2$
or $2=\left(v_1+2v_2\right)\dots$ (i)
By definition of coefficient of restitution,
$e=\frac{v_2-v_1}{u_1-u_2}$
or $e\left(u_1-u_2\right)=v_2-v_1$
$0.5(2-0)=v_2-v_1$...(ii)
$1=v_2-v_1$
Solving equations (i) and (ii), we get
$v_1=0m/s,v_2=1m/s$