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From a sphere of mass M and radius R, a smaller sphere of radius R2 is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is :
99386.jpg
  1. 59GM2450R2
  2. GM2225R2
  3. 41GM23600R2
  4. 41GM2450R2

A
GM2225R2
B
41GM23600R2
C
41GM2450R2
D
59GM2450R2
Solution
Verified by Toppr

If Mass of the sphere is M, Mass of the carved out sphere is MR3×(R2)3=M8
Consider the larger sphere to be made of positive mass M and negative mass M8
Net force on the +M8 sphere is
GMM8(3R)2+G(M8)(M8)(3RR2)2=GM2R2(1721400)=GM2R2(509400)=41GM23600R2

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