The direction of gravitational intensity at point P of a hemispherical shell of uniform mass desity is indicated by the arrow

Options

A. a
B. b
C. c
D. 0

Answer

C

Explanation

The gravitational potential is constant at all points inside a spherical shell. Therefore, the gravitational potential gradient at all points inside the spherical shell is zero [i.e., as V is constant, dV/dr = 0). Since gravitational intensity is equal to negative of the gravitational potential gradient, hence the gravitational intensity is zero at all points inside a hollow spherical shell. This indicates that the gravitational forces acting on a particle at any point inside a spherical shell, will be symmetrically placed. Therefore if we remove the upper hemi-spherical shell, the net gravitational force acting on the particle at the centre or at some other point P will be acting downwards which will also be the direction of gravitational intensity. It is so because, the gravitational intensity at a point is the gravitational force per unit mass at that point. Hence the gravitational intensity at the centre Q will be along c, i.e., option (iii) is correct.