A point mass m is situated inside a thick spherical shell of mass M, inner radius R and outer radius 2R. Work required to take this mass m from inside the shell to infinity, slowly is
A
GMm2R
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B
7GMm15R
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C
9GMm14R
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D
3GMm7R
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Solution
The correct option is C9GMm14R dV=−Gdmr=−Grρ4πr2drV=∫dV=−Gρ4π∫2RRrdr=−Gρ4π23R2whereρ=M43π(8R3−R3)=3M4π(7R3)⇒V=−9GM14RWorkdone=−V×m=9GMm14R