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`
.

Options

A. `(3GMm)/(2R^(2))`
B. `(2GMm)/(R^(2))`
C. `(GMm)/(R^(2))`
D. `(GMm)/(2R^(2))`

Answer

D

Explanation

`(E_(p)) = (GMd)/(R^(3)) + (G ((M)/(8)) ((R)/(2) - d))/(((R)/(2))^(3)) `
= `(GMd)/(R^(3)) + (GM ((R)/(2)))/(R^(3)) - (GMd)/(R^(3)) = (GM)/(2R^(2)) " " therefore "Force" = (GMm)/(2R^(2))`
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