Question

Let $V$ and $E$ denote the gravitational potential and gravitational field respectively, at a point due to certain uniform mass distribution described in four different situations of Column I. Assume the gravitational potential at infinity to be zero. The values of $E$ and $V$ are given in Column II. Match the statment in Column I with the results in Column Ii

Answer 1

Option A: The gravitational field inside a thin spherical shell is 0 by Gauss law for gravitation . Hence E=0. Since reference is taken at infinity, gravitational potential is non zero at center but it is constant inside the sphere.

Option B: At the center of solid sphere, E=0 since $E\alpha r$ inside the uniform solid sphere and hence E=0 at r=0. Since reference is taken at infinity, gravitational potential is non zero at center.

Option C: The gravitational field at the center of cavity in absence of cavity would be $\frac{GM}{R^3}$ . The material in the cavity would have no effect on field since the field at the center of a uniform sphere is zero. Hence $E\ne 0$. Also, since reference is taken at infinity, gravitational potential is non zero at center.

Option D: Each point mass will apply gravitational field in opposite direction and hence E=0. Since reference is taken at infinity, gravitational potential is non zero at center.

Answer is A>1,3 B>1,3 C>2,3 D>1,3.