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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

  • The M.I. of the solid sphere of density 'rho' and radius 'R' about an axis passing through its centre is given by

    A
    `(105)/(176)R^(2)rho`
    B
    `(176)/(105)R^(2)rho`
    C
    `(176)/(105)R^(5)rho`
    D
    `(105)/(132)R^(2)rho`

  • Inside a uniform sphere of mass M and radius R, a cavity of radius R//3 , is made in the sphere as shown :

    A
    Gravitational field inside the cavity is uniform
    B
    Gravitational field inside the cavity is non-uniform
    C
    The escape velocity of a particle projected from point A is `sqrt((88GM)/(15R))`
    D
    Escape velocity is defined for earth and particle system only

  • Inside a uniform sphere of density rho there is a spherical cavity whose centre is at a distance l from the centre of the sphere. Find the strength of the gravitational field inside the cavity.

    A
    `E=(-2)/3 piGrhol`
    B
    `E=(-4)/3piGrhol`
    C
    `E=(-4)/3pi^(2)Grhol`
    D
    `E=(-4)/3piGrho^(2)l^(2)`
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