A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance `sqrt3` a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

Options

A. `(GMm)/(8r^(2))`
B. `(GMm)/(4r^(2))`
C. ` sqrt(3) (GMm)/(8r^(2))`
D. `(GMm)/(8r^(3)sqrt(3) )`

Answer

C

Explanation

The gravitational field due to the ring at a distance `sqrt(3r)` is given by
`E = (Gm (sqrt(3)r))/([r^(2)+(sqrt(3r))^(2)]^(3//2)) rArr E = (sqrt(3)Gm)/(8r^(2))`
Attractive force = `(sqrt(3)"GmM")/(8r^(2))`