Question

Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $\sqrt{8}$$R$ is the distance between the centres of a ring (of mass $m$) and a sphere (of mass $M$) where both have equal radius $R$.

• A. $\frac{\sqrt{8}}{9}\frac{GmM}{R}$
• B. $\frac{\sqrt{8}}{27}\frac{GmM}{R^2}$
• C. $\sqrt{2}$ $\frac{GmM}{R^2}$
• D. $\frac{1}{3\sqrt{8}}\frac{GmM}{R^2}$

Answer 1

The correct option is B $\frac{\sqrt{8}}{27}\frac{GmM}{R^2}$

We know that ,

$F=ME=M\left(\frac{Gm\sqrt{8}R}{(R^2+(\sqrt{8R}{)}^2{)}^{\frac{3}{2}}}\right)$

[Assuming the sphere as a point mass located at its geometrical centre ]

$F=\frac{GmM\sqrt{8}R}{(9R^2{)}^{\frac{3}{2}}}=\frac{\sqrt{8}GmM}{(9R^2{)}^{\frac{3}{2}}}$

$F=\frac{\sqrt{8}GmM}{27R^2}$