A moving particle of mass $m$, makes a head on elastic collision with another particle of mass $2 m$, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to

• A

  $33 \%$
• B

  $67 \%$
• Correct answer
  C

  $90 \%$
• D

  $10 \%$

Solution

Fractional decrease in kinetic energy of mass $m$ $$ \begin{aligned} & =1-\left(\frac{m_2-m_1}{m_2+m_1}\right)^2=1-\left(\frac{2-1}{2+1}\right)^2 \\ & =1-\left(\frac{1}{3}\right)^2=1-\frac{1}{9}=\frac{8}{9} \end{aligned} $$

Hence, the correct answer is option: 'C'.