Question

A mass $M$ is broken in two parts : $m$ and (M- m). What would be the relation between $m$ and $M$ so that the force of gravitation between the two parts is maximum?

• A. $mM=2$
• B. $m=\frac{M}{2}$
• C. $M=m^2$
• D. none of these

Answer 1

Answer: (B)

$m=\frac{M}{2}$

Gravitational Force F= $\frac{Gm(M-m)}{r^2}$ where $r$ is distance between them.

For gravitational force to be maximum $\frac{dF}{dm}$ should be zero.

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

$\Rightarrow \frac{G}{r^2}(M-2m)$ =0

$\Rightarrow m=\frac{M}{2}$ $\because \frac{G}{r^2}$ is non zero constant.