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Question

From a solid sphere of mass M and radius R a spherical portion of radius R2 is removed, as shown in the figure. Taking gravitational potential V=0 at r=, the potential at the centre of the cavity thus formed is : (G= gravitational constant).
873435_3f5e1c8fc92c487cbf91967b41355518.png
  1. 2GM3R
  2. 2GMR
  3. GM2R
  4. GMR

A
2GM3R
B
GM2R
C
GMR
D
2GMR
Solution
Verified by Toppr

By superposition principle, v1=GM2R3[3R2(R2)2]
=11GM8R3
Also, v2=32G(M/8)(R/2)=3GM8R
The required potential is, v=v1v2
=11GM8R(3GM8R)
V=GMR

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