If mass M is split into two parts m and (M-m) which are then separated by a distance, the ratio of mass $\frac{M}{m}$ that maximises the gravitational force between the two parts is :

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1:4

1:2

1:1

2:1

answer is C.

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Detailed Solution

$F = \frac{Gm (M - m)}{r^{2}} = \frac{G}{r^{2}} (mM - m^{2})$ For F to be maximum $\frac{dF}{dm} = 0$ (as M and r are
constants) $\frac{d}{dm} [\frac{G}{r^{2}} (mM - m^{2})] = 0 i . e .,$ $M - 2 m = 0$ $\frac{m}{M} = \frac{1}{2}$ .

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