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A uniform solid of valume mass density r...

A uniform solid of valume mass density `rho` and radius R is shown in figure.

(a) Find the gravitational field at a point P inside the sphere at a distance r from the centre of the sphere. Represent the gravitational field vector `vec(l)` in terms of radius vector `vec(r )` of point P.
(b) Now a spherical cavity is made inside the solid sphere in such a way that the point P comes inside the cavity. The centre is at a distance a from the centre of solid sphere and point P is a distance of b from the centre of the cavity. Find the gravitational field `vec(E )` at point P in vector formulationand interpret the result.

Text Solution

Verified by Experts

(a) `(4pi G rho r)/(3), -(4)/(3)pi G rho vec(r )`
(b) `-(4)/(3)pi G rho vec(a)`, where `vec(a)` is position vector of centre of cavity w.r.t. centre of solid sphere.
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