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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

`(GrhopiR)/(3)`

B

`(2GppiR)/(3)`

C

`(4GrhopiR)/(3)`

D

`(3GrhopiR)/(2)`

Text Solution

Verified by Experts


Above distribution can be represented as shown in figure. Gravitational field due to sphere of radius R at a distance 3R
`E_(g)=(Grho(4)/(3)piR^(3))/(4R^(2))=(GrhopiR)/(3)`
so net field at center will be `2F_(g)=(2GrhopiR)/(3)`
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Knowledge Check

  • A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F_(1) on a particle placed at P , distance 2R from the centre O of the sphere. A spherical cavity of radius R//2 is now made in the sphere as shown in figure. The particle with cavity now applies a gravitational force F_(2) on same particle placed at P . The radio F_(2)//F_(1) will be

    A
    `1//2`
    B
    `7//9`
    C
    `3`
    D
    `7`

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