Q.

The gravitational potential of two homogenous spherical shells A and B of same surface density at their respective centres are in the ratio 3:4. If the two shells coalesce into a single one such that surface mass density remains the same, then the ratio of potential at an internal point of the new shell to shell A is equal to

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a

3:2

b

4:3

c

5:3

d

5:6

answer is C.

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Detailed Solution

MA=σ4πRA2, MB=σ4πRB2where σ is surface density.⇒ VA=−GMARA, VB=−GMBRBVAVB=MAMBRBRA=σ4πRA2σ4πRB2.RBRA=RARBGiven VAVB=MAMB=34Then RB=43RAFor new shell of mass M and radius R,           M=MA+MB=σ4πRA2+σ4πRB2           σ4πR2=σ4πRA2+RB2Then  VVA=MRARMA=σ4πRA2+RB2RA2+RB212RAσ4πRA2=RA2+RB2RA=53
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