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Question

A gravity of radius R/2 is made inside a solid sphere of radius R. The center of the gravity is located at a distance R/2 from the center of the sphere. The gravitational force on a particle of mass m at a distance R/2 from the center of the sphere on the line joining both the centers of the sphere and the gravity is (opposite to the center of the gravity)[Here g=(GM)/R2, where M is the mass of the sphere]

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Solution

The correct option is **B** 3mg8

Consider the figure

Consider the figure

Gravitational force inside a solid sphere =GMmR3×r.....(1)

Where r is distance from centre.

Gravitational force due to solid sphere outside=GMmr2....(2) where r is distance from centre.

Gravitational force due to remaining body = gravitational force due to 9 solid sphere due to cavity)

Mass of material inside cavity

=M1=M×43π(R2)343πR3=M8

∴Fbody=GMmR3×(R2)−GMm8(R1)2

GMm2R2−GMm8R2GMR2.m(12−18)mg.(4−18)=3mg8=Fbody

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