Question

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

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

Answer 1

Answer: (A)

Here, $m _{1}= w , m _{2}=2 m$
$u _{1}=2 m / s , u _{2}=0$
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
$m_{1} u_{1}+m_{2} u_{2}=m_{1} v_{1}+m_{2} v_{2}$
$\therefore m \times 2+2 m \times 0=m \times v_{1}+2 m \times v_{2}$
or $2 m=m v_{1}+2 m v_{2}$
or $2=\left(v_{1}+2 v_{2}\right) \ldots$ (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
$v_{1}=0 \,m / s , v_{2}=1 \,m / s$