Question

A metal ball of mass $2kg$ moving with speed of $36km/h$ is having a collision with a stationary ball of mass $3kg$. If after collision, both the balls move together, the loss in kinetic energy due to collision is

• A. $80J$
  
• B. $40J$
  
• C. $60J$
  
• D. $160J$
  

Answer 1

The correct option is C $60J$

Mass of metal ball $m_1=2kg$ and its speed before collision $u_1=36km/h=10m/s$

Mass of stationary ball $m_2=3kg$ and its speed before collision $u_2=0m/s$

Since the two balls move together after collision, thus the collision is perfectly inelastic.

Kinetic energy lost in perfectly inelastic collision $\Delta KE=\frac{1}{2}\frac{m_1{m}_2}{(m_1+m_2)}(u_1-u_2{)}^2$

$\therefore$ $\Delta KE=\frac{1}{2}\frac{\left(2\right)\left(3\right)}{(2+3)}(10-0{)}^2=60J$