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A mass M is split into two parts m and $(M - m)$ and then they are separated by a certain distance. If the gravitational force between them is to be maximum,

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$m = \frac{M}{3}$

$m = \frac{M}{4}$

$m = \frac{M}{2}$

$m = 0$

answer is C.

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Detailed Solution

F to be maximum

$\frac{dF}{dm} = 0$

$\frac{d}{dm} [\frac{G (M - m) m}{r^{2}}] = 0$

$M - 2 m = 0$

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