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A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts

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Detailed Solution

$F = \frac{Gm (M - m)}{r^{2}}$
For maximum force $\frac{dF}{dm} = 0$
$\Rightarrow \frac{d}{dm} (\frac{GmM}{r^{2}} - \frac{{Gm}^{2}}{r^{2}}) = 0$
$\Rightarrow M - 2 m = 0 \Rightarrow \frac{m}{M} = \frac{1}{2}$

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