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Question

A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance 3a from the centre will be

A
GM9a2
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B
2GM3a2
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C
2GM9a2
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D
GM3a2
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Solution

The correct option is D GM3a2
Gravitational field at point P, which is at a distance of 3a from the center of the sphere.
EP=Gravitational field due to sphere of mass M + Spherical shell of mass 2M
EP=GM(3a)2+G(2M)(3a)2=GM3a2

For a part on the surface of a spherical uniform charge distribution the whole mass acts as a point mass kept at the centre.
Hence option (C) is correct.

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