Question

A mass M is split into two parts, m and (M-m), which are then separated by a certain distance. What ratio of $\frac{m}{M}$ maximizes the gravitational force between the two parts

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B

$\frac{1}{2}$

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