Question

A metal ball of mass $2kg$ moving with velocity of $36km/h$ has a head on collision with a stationary ball of mass $3kg$. If after the collision the two balls moves together, the loss in kinetic energy due to collision is (in J)

• A. $140$
  
• B. $100$
  
• C. $60$
  
• D. $40$
  

Answer 1

The correct option is C $60$

Given : $m_1=2kg$ $u_1=36km/h=36\times \frac{5}{18}=10m/s$

Also, $m_3=3kg$ $u_2=0m/s$

Since the balls move together with same velocity after collision, $e=0$

Loss in kinetic energy $\Delta K.E.=\frac{1}{2}\left(\frac{m_1{m}_2}{m_1+m_2}\right)(1-e^2)(u_1-u_2{)}^2$

$⟹$ $\Delta K.E.=\frac{1}{2}\left(\frac{2\times 3}{2+3}\right)(1-0)(10-0{)}^2=60J$