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Q64. 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

a 11GMmR2 (b) 14 GMmR2c GMm2R2 (d) GMmR2

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Solution

Dear student
gravitational field in the cavity is E=4πGρ3(C1C2 ) (C1 and C2 are the centres of the sphere and the cavity)ρ=M43πR3 and C1C2=distance between the centres=R2E=4πG×M3×43πR3(R2)E=G×MR2(12)so force acting on the charge isF=mEF=G×m×M2R2Regards

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