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

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mg2

3mg8

mg16

None of these

answer is B.

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Detailed Solution

gnet=g1−g2=GmR2R3−Gm8R2=Gm2R2−Gm8R2=Gm2R21−14=Gm2R234=3Gm8R2F=mg=3GMm8R2=3mg8

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