Question

A uniform ring of mass $m$ and radius $r$ is placed directly above a uniform sphere of mass $M$ and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance $r\sqrt{3}$ as shown in the figure.
The gravitational force exerted by the sphere on the ring will be

• A. $\frac{GMm}{8r^2}$
• B. $\frac{GMm}{4r^2}$
• C. $\sqrt{3}\frac{GMm}{8r^2}$
• D. $\frac{GMm}{8r^2\sqrt{3}}$

Answer 1

Answer: (C)

The gravitational field due to the ring at a distance $\sqrt{3}r$ is given by