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.

Answer

A, B, C

Explanation

`dF =` force on a small mass 'dm' of the ring by the sphere.

Net force on ring `= sum (dF sin theta)` or `int dF sin theta`
`= sum (GM(dm))/((2a)^(2)) xx sqrt(3)/(2) = (sqrt(3) GM)/(8a^(2)) sum (dm)`
But `sum (dm) = m`, the mass of whole ring.
`:.` Net force `= (sqrt(3) GMm)/(8a^(2))`