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Question

The magnitudes of the gravitational field at distances r1 and r2 from the centre of a uniform sphere of radius R and mass M are F1 and F2, respectively. Then.

A
F1F2=r1r2 if r1<R and r2<R
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B
r22r2 if r1>R and r2>R
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C
F1F2=r1r2 if r1>R and r2>R
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D
F1F2=r21r22 if r1<R and r2<R
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Solution

The correct options are
A F1F2=r1r2 if r1<R and r2<R
B r22r2 if r1>R and r2>R
For a solid sphere of mass M and radius R -
Gravitational field =GMr2 ( r> Radius of sphere )
=GMrR3 (r<R)
If r1<R and r2<R
F1=GMr1R3 and F2=GMr2R3
F1F2=r1r2
Option (A) is correct.

If r1<R and r2<R
F1=GMR21 and F2=GMR22
F1F2=r22r21
Hence, option A and B correct.

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