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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]

A
mg2
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B
3mg8
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C
mg16
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D
None of these
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Solution

## The correct option is B 3mg8Consider 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)2GMm2R2−GMm8R2GMR2.m(12−18)mg.(4−18)=3mg8=Fbody

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