Question

A ring of mass m and radius R and a sphere of mass M and same radius R are separated by a distance $\sqrt{8}R$ as shown in the figure. The force of attraction between the ring and the sphere is

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

Answer 1

The correct option is A

$\frac{2\sqrt{2}}{27}\frac{GmM}{R^2}$

The sphere will behave as a point mass placed at its centre. So, effectively we have to find the force exerted on a point mass M at a distance $\sqrt{8}R$ on the axis of the ring.
Now, electric field at point B because of the ring, $E=\frac{Gm\sqrt{8}R}{{[R^2+(\sqrt{8}R{)}^2]}^{\frac{3}{2}}}=\frac{2\sqrt{2}Gm}{27R^2}$
Now, force on the sphere, $F=ME=\frac{2\sqrt{2}GmM}{27R^2}$
Hence, the correct choice is (a).