The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. 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

Explanation

Consider the diagram, density of the shell is constant
Let it is `rho`

Mass of the shell = (density) `xx` (volume)
`= (rho) xx (4)/(3) pi R^(3) = M`
As the density of the shell is uniform, it can be treated as a point mass placed at its centre. Therefore, `F =` gravitational force between M and `m = (GMm)/(r^(2))`
`F = 0 " for " r lt R` (i.e, force inside the shell is zero)
`= (GM)/(r^(2)) " for " r ge R`
The variation of F versus r is shown in the diagram.