Centre of Mass 3 Question 16
19. 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 two fragment of masses $m / 4$ and $3 m / 4$. An instant later, the smaller fragment is at $y=+15 cm$. The larger fragment at this instant is at
(1997 C, 1M)
(a) $y=-5 cm$
(b) $y=+20 cm$
(c) $y=+5 cm$
(d) $y=-20 cm$
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Answer:
Correct Answer: 19. (a)
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, $\quad y _{CM}=\frac{m _1 y _1+m _2 y _2}{m _1+m _2}$
Therefore, $0=\frac{(m / 4)(+15)+(3 m / 4)(y)}{(m / 4+3 m / 4)}$
or
$$ y=-5 cm $$
