Question

4.(a) Explain why the force exerted on a particle by a uniform sphere must be directed toward the centre of the sphere. (b) Would this statement be true if the mass distribution of the sphere were not spherically symmetric? Explain.

Short answer

(a) The force exerted on a particle by a uniform sphere is perpendicular towards the centre of the sphere.

(b) No, the above statement doesn’t satisfy the spherically symmetric.

Step-by-step solution

Spherically Symmetric.

Spherically symmetric means the body has the shape of a sphere and the parts are arranged concentrically around or radiate from the centre of the sphere.

Every point “q” on the sphere that does not lie along the axis connecting the centre of the sphere and the particle will have a companion point “q” for which the components of the gravitational force perpendicular to the axis will cancel.

Point “q” can be found by rotating the sphere 180° about the axis.

Mass distribution of spheres

The force will not necessarily cancel if the mass is not uniformly distributed unless the centre mass of the non-uniform sphere still lies along the axis.

Therefore, the mass is not distributed on the spherically symmetric surface.