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The gravitational field inside a sphere which carries a volume mass density proportional to the distance (r) from the origin $ρ = a r$ ( $a$ is a constant) at distance ‘r’ is:

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Ga r3

Ga r2

Ga r23

Gπα r2

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detailed solution

Correct option is D

dm=ρ4πr2dr ⇒m=πar4 E=Gmr2=Gπar2

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The gravitational field inside a sphere which carries a volume mass density proportional to the distance (r) from the origin ρ=a r (a is a constant) at distance ‘r’ is:

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Ready to Test Your Skills?

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The gravitational field inside a sphere which carries a volume mass density proportional to the distance (r) from the origin $ρ = a r$ ( $a$ is a constant) at distance ‘r’ is: