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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 maximise the gravitational force between the parts?

\[(a)\;\frac{2}{3} \quad (b)\;\frac{3}{4} \quad (c)\;\frac{1}{3} \quad (d)\;\frac{1}{2} \]

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1 Answer

Let r be the direction between the parts
$F= \large\frac{Gm(M-m)}{r^2}$
$\qquad= \large\frac{G}{r^2} $$(mM-m^2)$
The force will be maximum
ie $\large\frac{d}{dm} \bigg[\large\frac{G}{r^2} $$(mM-m^2)\bigg]=0$
or $\large\frac{m}{M}=\large\frac{1}{2}$
Hence d is the correct answer.


answered Aug 23, 2013 by meena.p
edited Feb 17, 2014 by meena.p

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