The gravitational potential of two homogeneous spherical shells A and B, having the same surface mass density, at their respective centres are in the ratio 3 : 4 . If the two shells coalesce into sing

Question

The gravitational potential of two homogeneous spherical shells A and B, having the same surface mass density, at their respective centres are in the ratio 3 : 4 . If the two shells coalesce into single one such that the surface mass density remains the same, then the ratio of potential at an internal point of the new shell and A is equal to

TestHub · Accepted Answer

M A = σ 4 π R A 2 , M B = σ 4 π R B 2 where σ is surface density V A = - G M A R A , V B = - G M B R B V A V B = M A M B R B R A = σ 4 π R A 2 σ 4 π R B 2 R B R A = R A R B Given V A V B = R A R B = 3 4 then R B = 4 3 R A For new shell of mass M and Radius R - V V A = R R A = R A 2 + R B 2 R A = 5 3

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