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The gravitational force between a hollow...

The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is E. Show the nature of F versus r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density. 

Text Solution

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`implies` Take density of the shell `(rho)` is constant.

Mass of the shell = (density) `xx` (volume) 
`(rho) xx 4/3 piR^(3) = M`
As the density of the shell is uniform, it can be treated as a point mass placed at its centre.
Now, gravitational force between `M and M_D`
`F = (GMm)/r^(r ge R)`
`F = 0 (r lt R)`
The relation of F versus r is shown in the diagram.
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