Gravitation Question 363

Question: 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 charge density remains same, then the ratio of potential at an internal point of the view shell to shell A is equal to

Options:

A) 3:2

B)4:3

C) 5:3

D)5:6

Show Answer

Answer:

Correct Answer: C

Solution:

  • [MA=σ4πR2A,MB=σ4πR] , where a is surface density

    [VA=GMARA,,VB=GMBRB]

    [VAVB=MAMB,,RBRA=σ4πRA2σ4πRB2,RBRA=RARB]

    Given [VAVB=,RARB=34]

    then [RB=43RA]

    for new shell of mass M and radius R [M=MA+MB=σ4πRA2+σ4πRB2]

    [σ4πR2=σ4π(RA2+R2B)]

    then [VVA=MM,,RARB=σ4π(RA2+RB2)(RA2+RB2)1/2,=RAσ4πRA2]

    [RA2+RB2RA=53]



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