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

Let us consider a point mass m is placed at a distance r from the centre of a hollow spherical shell mass M, uniform density `sigma` and radius R. Gravitational force between them is
`F = (GmM)/(r^(2)) " "[M = 4pi R^(2) sigma]`
`F = (Gm)/(r^(2))(4pi R^(2) sigma) " "[because M = (4)/(3)pi R^(3) rho]`
or `F prop (1)/(r^(2))`
Inside the hollow spherical shell F is zero. The variation of F with r is shown in figure.