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JEE Main 2013 (23 Apr, Shift 1) · Motion of Centre of Mass

Motion of Centre of Mass question from JEE Main 2013 (23 Apr, Shift 1)

Q10JEE Main 2013 · 23 APR · SHIFT 1Medium

Motion of Centre of Mass

A projectile of mass M is fired so that the horizontal range is 4 km. At the highest point the projectile explodes in two parts of masses M/4 and 3M/4 respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is:

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Answer: (c)

The explosion is internal, so the CM still lands at the original range, 4 km.
The heavier part $\frac{3M}{4}$ falls vertically from the highest point, landing at 2 km.
$M(4) = \frac{3M}{4}(2) + \frac{M}{4}x \Rightarrow 4 = 1.5 + \frac{x}{4}$
$x = 10$ km, so the answer is (c).

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