Question

An isolated particle of mass m is moving in horizontal plane $[x-y]$ along the x-axis at a certain height above the ground. It suddenly explodes into fragments of masses $m/4$ and $3m/4$. An instant later the smaller fragment is at $y=15cm$. The larger fragment at this instant is at:

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

Answer 1

The correct option is A $y=-5$ cm

Before explosion particle was moving along x-axis i.e. it has no y-component of velocity. Therefore the centre of
mass will not move in y-direction or we can say $y_{cm}=0$
Now $y_{cm}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$
$0=\frac{\left(\frac{m}{4}\right)(+15)+\left(\frac{3m}{4}\right)y}{(\frac{m}{4}+\frac{3m}{4})}\Rightarrow y=-5cm$