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The mass density of a planet of radius R  varies with the distance   r from its centre as ρ ( r ) = ρ 0 1 - r 2 R 2   . Then the gravitational field is maximum at:

Option 1 -

r = 1 3 R

Option 2 -

r = R

Option 3 -

r = 5 9 R

Option 4 -

r = 3 4 R

0 3 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    2 months ago
    Correct Option - 3


    Detailed Solution:

    E = G m enc   r 2 = G r 2 ∫ 0 r ? ρ 0 1 - r 2 R 2 4 π r 2 d r

    E = G r 2 4 π ρ 0 r 3 3 - r 5 5 R 2 0 r = 4 π G ρ 0 r 3 - r 3 5 R 2

    For E  to be m a x , d E d r = 0

    ⇒ 1 3 - 3 r 2 5 R 2 = 0 r = 5 9 R

     

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