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# 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).−2GM3R−2GMR−GM2R−GMR

A
2GM3R
B
GM2R
C
GMR
D
2GMR
Solution
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#### By superposition principle, v1=−GM2R3[3R2−(R2)2]=−11GM8R3Also, v2=−32G(M/8)(R/2)=−3GM8RThe required potential is, v=v1−v2=−11GM8R−(−3GM8R)V=−GMR

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