Question

A mass M is broken in two parts: m and (M -m). Relation between m and M so that the force of gravitation between the two parts is maximum is.

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

Answer 1

The correct option is B $m=\frac{M}{2}$

The force of gravitational between the two masses is

$F=\frac{G(M-m)m}{R^2}$

Distance remaining the same, we need to maximize F for different values of m.

$\frac{dF}{dm}=0$, $\frac{d}{dm}(\frac{GMm}{R^2}-\frac{G{m}^2}{R^2})=0$

$\frac{GM}{R^2}-\frac{2Gm}{R^2}=0$

$\frac{GM}{R^2}=\frac{2Gm}{R^2}$

$M=2m$

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