A mass $M$ is broken into two parts $m$ and ( $M-m$ ). What should be the ratio between $m$ and $M$

Question

A mass $M$ is broken into two parts $m$ and ( $M-m$ ). What should be the ratio between $m$ and $M$ so that the force of gravitation between them, is maximum\

Professor PC Thomas Classes · Answer

$\mathrm{F}=\mathrm{G} \frac{\mathrm{m}(\mathrm{M}-\mathrm{m})}{\mathrm{d}^{2}}$ F will be maximum when $m(M-m)$ is maximum. ie. $m=M-m$ \Find the answer\ Note:- When the sum of masses of two quantities is a constant the product will be a maximum when the quantities are equal\