A ball moving with velocity $2 \mathrm{~m} / \mathrm{s}$ collides head on with another stationary ba

Question

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

Professor PC Thomas Classes · Answer

(a) : Here, $m_{1}=m, m_{2}=2 m$ 
$ u_{1}=2 \mathrm{~m} / \mathrm{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 
$m_1 u_1+m_2 u_2=m_1 v_1+m_2 v_2$ ....(i)
 $	herefore \quad m 	imes 2+2 m 	imes 0=m 	imes v_{1}+2 m 	imes v_{2}$\ or $2 m=m v_{1}+2 m v_{2}$ or $2=\left(v_{1}+2 v_{2}ight)$\ By definition of coefficient of restitution, 
$ e=\frac{v_{2}-v_{1}}{u_{1}-u_{2}} $ 
or $\quad e\left(u_{1}-u_{2}ight)=v_{2}-v_{1}$\ $\Rightarrow \quad 0.5(2-0)=v_{2}-v_{1}$\ Solving equations (i) and (ii), we get 
$ v_{1}=0 \mathrm{~m} / \mathrm{s}, v_{2}=1 \mathrm{~m} / \mathrm{s} $