Question

A particle of mass $m$positioned at origin of a horizontal plane $(x-y)$, suddenly explodes into two fragments of masses $m/4\text{and}3m/4$. An instant later, the smaller fragment is at $y=+15cm.$ The larger fragment at this instant is at (Assuming the particles after explosion move in horizontal plane and neglect effect of gravity)

• A. $y=–5cm$
  
• B. $y=+20cm$
• C. $y=+5cm$
• D. $y=-20cm$

Answer 1

The correct option is A $y=–5cm$


Since there is no external force acting on the particle, position of centre of mass does not change.

Position of centre of mass before collision = position of centre of mass after collision
hence,
$y_{cm}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}=0$
Where, $y_1$is position of smaller mass after collision,
$y_2$ is position of centre of mass of larger mass after collision
$\therefore \left(\frac{m}{4}\right)\times (+15)+\left(\frac{3m}{4}\right)\left(y_2\right)=0\Rightarrow y_2=-5cm$