Question

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 vs. r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.

Answer 1

Formula used: $F=\frac{G{m}_1{m}_2}{r^2}$

Let the mass of spherical shell be $M$ and mass of point object is $m.$

Then gravitational force between hollow shell and point mass,

$F=\frac{GMm}{r^2}$

Here, r is the distance between the point mass and center of the shell.

As the given sphere is hollow, so mass is distributed on the surface of the sphere.

Hence, force inside the shell will be zero.

$F=0$ for $0<r<R$

And $F=\frac{GMm}{r^2}$ is true for $r\ge R$

Force will be maximum at the surface of the shell and becomes zero if r tends to infinity.

So, the variation of $F$ vs $r$ will be as shown,