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A solid sphere of mass M and radius R has a spherical cavity of radius R/2 such that the centre of cavity is at a distance R/2 from the centre of the sphere. A point mass m is placed inside the cavity at a distance R/4 from the centre of sphere. The gravitational force on mass m is

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a

11GMmR2

b

14GMmR2

c

GMm2R2

d

GMmR2

answer is C.

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Detailed Solution

Field strength is uniform inside the cavity. Let us find its value at centre.ET=EO+EC(T= Total ,O= Remaining ,C= Cavity )∴ EO=ET-EC=GMR3R2-0=GM2R2∴ F=mFR=GMm2R2

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