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  4. A mass M is split into two parts m and (.M-m.) , which are then separated by a certain distance. The ratio m:M which maximizes the gravitational force between the parts is

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Q. A mass $M$ is split into two parts $m$ and $\left(\right.M-m\left.\right)$ , which are then separated by a certain distance. The ratio $m:M$ which maximizes the gravitational force between the parts is

NTA AbhyasNTA Abhyas 2022

Solution:

$F=\frac{G m \left(\right. M - m \left.\right)}{x^{2}};$ For maxima,
$\frac{d F}{d m}=\frac{G}{x^{2}}\left(M - 2 m\right)=0$
or $\frac{m}{M}=\frac{1}{2}$