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Q.

The gravitational potential of two homogeneous 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 single one such that surface density remains 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

4πr2ρ=4πr12ρ+4πr22ρ⇒r2=r12+r22V=−GMr=−G4πr2ρrV=−4πrGρ⇒V∝r⇒V1V2=r1r2=34⇒r12r22=916r12:r22:r2=r12:r22:r12+r22=9:16:(9+16)⇒r1:r2:r=3:4:5=V1:V2:V
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