Question

A ball moving with velocity $2m/s$ collides head on with another stationary ball of double the mass. If 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

The correct option is A $0,1$

Let mass of first ball be $m$ i.e. $m_1=m$

Mass of second ball $m_2=2m$

Velocity of first ball before collision $u_1=2m/s$

Velocity of second ball before collision $u_2=0m/s$

Given : $e=0.5$

So, velocity of first ball after collision $v_1=\frac{(m_1-e{m}_2)u_1+(1+e)m_2{u}_2}{m_1+m_2}$

$\therefore$ $v_1=\frac{[m-0.5(2m\left)\right]\left(2\right)+(1+0.5)\left(2m\right)\left(0\right)}{m+2m}=0m/s$

Velocity of second ball after collision $v_2=\frac{(m_2-e{m}_1)u_2+(1+e)m_1{u}_1}{m_1+m_2}$

$\therefore$ $v_2=\frac{[2m-0.5m]\left(0\right)+(1+0.5)\left(m\right)\left(2\right)}{m+2m}=1m/s$

Correct answer is option A.