Question

A uniform ring of mass M and radius R is placed directly above a uniform sphere of mass 8 M and of same radius R. The centre of the ring is at a distance of $d=\sqrt{3}R$from the centre of the sphere. The gravitational attraction between the sphere and the ring is

• A. $\frac{8G{M}^2}{R^2}$
• B. $\frac{2G{M}^2}{\sqrt{3}{R}^2}$
• C. $\frac{3G{M}^2}{2R^2}$
• D. $\frac{\sqrt{3}G{M}^2}{R^2}$

Answer 1

The correct option is D

$\frac{\sqrt{3}G{M}^2}{R^2}$

$\text{Gravitational field due to the ring at a distance}d=\sqrt{3}R\text{on its axis is}:$

$E=\frac{GMd}{(R^2+d^2{)}^{2/3}}=\frac{\sqrt{3}GM}{8R^2}\text{Force on sphere}=8ME=\frac{\sqrt{3}G{M}^2}{R^2}$