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

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

UP CPMTUP CPMT 2015System of Particles and Rotational Motion

Solution:

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, $y_{ CM }=\frac{m_{1} y_{1}+m_{2} y_{2}}{m_{1}+m_{2}}$
Therefore, $0=\frac{(m / 4)(+15)+(3 m / 4)(y)}{(m / 4+3 \,m / 4)}$
or $y=-5 \,cm$