Question

Two objects of masses $m$ and $4m$ are at rest at an infinite separation. They move towards each other under mutual gravitational attraction. If $G$ is the universal gravitational constant. Then separation $r$ would be .............( if the force between them is 50 N)

Answer 1

Force between the two masses,

$F=\frac{G4m^2}{r^2}$

$r^2=\frac{4G{m}^2}{F}$

$r=\sqrt{\frac{4G{m}^2}{F}},F=50N$

$=\sqrt{\frac{4G{m}^2}{50}}$

$r=\sqrt{\frac{2G{m}^2}{25}}$