Question

Three particles P, Q and R are placed as per given figure Masses of P, Q and R are $\sqrt{3}m,$ $\sqrt{3}m$ and m respectively. The gravitational force on a forth particles S of mass M is equal to _

Answer 1

Gravitational force on forth particle S is

$F_S=\frac{G{m}_P{m}_R}{n^2}$

$F_S=\frac{G\times \sqrt{3}m\times m}{(\sqrt{3}d{)}^2}$

$F_S=\frac{G\times \sqrt{3}m\times m}{3d^2}$

$=\frac{G\sqrt{3}{m}^2}{3d^2}=\frac{G{m}^2}{\sqrt{3}{d}^2}$

Hence,

Gravitational force on forth particle S is

$F_S=\frac{G{m}^2}{\sqrt{3}{d}^2}$