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Consider a solid sphere of density rho a...

Consider a solid sphere of density `rho` and radius `4R`. Centre of the sphere is at origin. Two spherical cavities centred at `(2R,0)` and `(-2R,0)` are created in sphere. Radii of both cavities is `R`. In left cavity material of density `2rho` is filled while second cavity is kept empty. What is gravitational field at origin.

A

`(4GrhopiR)/3`

B

`(3GrhopiR)/2`

C

`(GrhopiR)/3`

D

`(2GrhopiR)/3`

Text Solution

Verified by Experts

The correct Answer is:
D
Above distribution canbe represented as shown in figure
Gravitation field due to sphere of radius `R` at a distance `2R`.
`E_(g)=(Grho 4/3piR^(3))/(4R^(2))=(GrhopiR)/3`
So net field at centre will be`2F_(g)=(2GrhopiR)/3`
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