Question

An isolated particle of mass $m$ is moving in horizontal plane $x-y$, along the x-axis, at a certain height above ground. It suddenly explodes into two fragments of masses $\frac{m}{4}$ and $\frac{3m}{4}$ . An instant later, the smaller fragment is at $y=+15\text{cm}$. The larger fragment at this instant is at

• A. $y=-5\text{cm}$
• B. $y=+5\text{cm}$
• C. $y=-50\text{cm}$
• D. $y=-20\text{cm}$

Answer 1

The correct option is A $y=-5\text{cm}$

$\therefore$ 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 $\Delta y_{com}=0$.
Now, $\Delta y_{com}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$
Therefore, $0=\frac{\left(\frac{m}{4}\right)(+15)+\left(\frac{3m}{4}\right)\left(y\right)}{(\frac{m}{4}+\frac{3m}{4})}$
$y=-5\text{cm}$
$\therefore \left(a\right)$