A uniform ring of mass m and radius a is placed directly above a uniform sphere of mass M and of equal to radius. The centre of the ring is at a distance 3 a from the centre of the sphere. The gravitational force (F) exerted by the sphere on the ring is

Step-by-step solution

Now, the gravitational field due to the ring at a distance d= 3 a on its axis is E= G m d (a^2+d^2 )^ 3 / 2 = 3 G m 8 a^2 The force in a particle of mass M placed here is F=M E= 3 G M m 8 a^2 This is also the force due to the sphere in the ring.