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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 centered 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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