Question

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

• A. $1:4$
• B. $1:3$
• C. $1:2$
• D. $1:1$

Answer 1

The correct option is C $1:2$

Gravitational force between two parts $F=\frac{Gm(M-m)}{r^2}$

For maxima, $\frac{dF}{dm}=0$

Or $\frac{d}{dm}.\frac{Gm(M-m)}{r^2}=0$

Or $\frac{d}{dm}(mM-m^2)=0$

Or $M-2m=0$ $⟹m=\frac{M}{2}$

Hence force between them is maximum when $m:M=1:2$