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A spherical hollow cavity is made in a l...

A spherical hollow cavity is made in a lead sphere of radius `R` such that is surface touches the outside surface of the lead sphere and passes through its centre. The mass of the sphere before hollowing was `M` with what gravitational force will the hollowed out lead sphere attract a small sphere of mass m which lies at a distacne d from the centre of the lead sphere on the straight line connecting the centeres of the spheres and that of the hollow if `d =2R`
.

A

`(7GMm)/(18R^(2))`

B

`(7GMm)/(36R^(2))`

C

`(7GMm)/(9R^(2))`

D

`(7GMm)/(72R^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • A spherical hollow is made in a lead sphere of radius R such that its surface touches the outside surface of the lead sphere and passes through the centre. The mass of the lead sphere before hollowing was M . The force of attraction that this sphere would exert on a particle of mass m which lies at a distance d from the centre joining the centre of the sphere and the hollow is

    A
    `(GMm)/(d^(2))`
    B
    `(GMm)/(d^(2))[1-1/(8(1-R/(2d))^(2))]`
    C
    `(GMm)/(d^(2))[1-1/(8(1+R/(2d))^(2))]`
    D
    `(GMm)/(8d^(2))`

  • A spherical cavity is made in a lead sphere of radius R such that its surface touches the outsides surface of lead sphere and passes through the centre. The shift in the centre of mass of the lead sphere as a result of this following, is

    A
    `(R)/(7)`
    B
    `(R)/(14)`
    C
    `(R)/(2)`
    D
    R

  • A spherical hole is made in a solid sphere of radius R. The mass of the sphere before hollowing was M. The gravitational field at the centre of the hole due to the remaining mass is

    A
    zero
    B
    `(GM)/(8R^(2))`
    C
    `(GM)/(2R^(2))`
    D
    `(GM)/(R^(2))`