Question

A uniform ring of mass m is lying at a distance 1.73 a from the centre of a sphere of mass M just over the sphere where a is the small radius of the ring as well as that of the sphere. Then gravitational

force exerted is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

dF sin $\theta$ will get cancelled

$\therefore$ d $F_{net}$ = dF cos $\theta$ = (dm)E cos $\theta$

= (dm) $\frac{GM\frac{\sqrt{3}}{2}}{\sqrt{a^2+{{(\sqrt{3a}}^2)}^2}}$

$\therefore$ $F_{net}$ = $\int$ d $F_{net}$

= $\frac{\sqrt{3}}{8}$ $\frac{Gmm}{a^2}$

mass of the earth $m_1$ = M, Mass of the moon $m_2$ = $\frac{M}{81}$ and distance between earth & moon d = 60R