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`
.

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

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

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

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

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The correct Answer is:

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

`(GMm)/(d^(2))`

`(GMm)/(d^(2))[1-1/(8(1-R/(2d))^(2))]`

`(GMm)/(d^(2))[1-1/(8(1+R/(2d))^(2))]`

`(GMm)/(8d^(2))`

`(R)/(7)`

`(R)/(14)`

`(R)/(2)`

zero

`(GM)/(8R^(2))`

`(GM)/(2R^(2))`

`(GM)/(R^(2))`