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Q.

From a uniform sphere of radius ‘R’ a spherical cavity of radius  R2 is removed from the edge as shown. The mass of the sphere after removing cavity is  M0. Consider points A, B, C, D. Assume potential at infinity is zero. ‘C’ is the centre of the cavity and AB = R
Question Image

 Column – I  Column – II
A)The gravitational field at A is ‘g’. Then  gR2GM0 is(P)87
B)The gravitational potential at B is V. Then  VRGM0 is(Q)47
C)The gravitational potential at C is V. Then  VRGM0 is(R)6863
D)The gravitational field at D is ‘g’. Then  gR2GM0  is  (S)107
  T) Zero 

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a

A – R; B – S; C – P; D – Q 

b

A – Q; B – P; C – S; D – R 

c

A – S; B – R; C – T; D – Q

d

A – R; B – Q; C – S; D – T

answer is A.

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Detailed Solution

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The mass of the complete sphere is  8M07, the mass in the cavity is  M07
Gravitational potential  V=GM2R3(3R2r2)
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