Question

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 maximizes the gravitational force between the two parts

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$F=\frac{Gm(M-m)}{r^2}Formaximumforce\frac{dF}{dm}=0\Rightarrow \frac{d}{dm}(\frac{GmM}{r^2}-\frac{G{m}^2}{r^2})=0\Rightarrow M-2m=0\Rightarrow \frac{m}{M}=\frac{1}{2}$