A uniform ring of mass M and radius r is placed directly above a uniform sphere of mass 8 M and of same radius R. The centre of the ring is at a distance of d = 3 R from the centre of the sphere. The gravitational attraction between the sphere and the ring is
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a
GM2R2
b
3GM22R2
c
2GM22R2
d
3GM2R2
answer is D.
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Detailed Solution
From the figure, the gravitational intensity due to the ring at a distance d=3R on its axis is I=GMd2+R23/2 =GM×3R3R2+R23/2=3GM8R2 Force on sphere=(8M)I=(8M)×3M8R2=3GM2R2