Question

For the above problem, the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow.

• A. d
• B. e
• C. f
• D. g

Answer 1

The Correct Option is B

Gravitational potential (V) is constant at all points in a spherical shell. Hence, the gravitational potential gradient \((\frac{dV}{dr})\) is zero everywhere inside the spherical shell. The gravitational potential gradient is equal to the negative of gravitational intensity. Hence, intensity is also zero at all points inside the spherical shell. This indicates that gravitational forces acting at a point in a spherical shell are symmetric.

If the upper half of a spherical shell is cut out (as shown in the given figure), then the net gravitational force acting on a particle at an arbitrary point P will be in the downward direction. 

Since gravitational intensity at a point is defined as the gravitational force per unit mass at that point, it will also act in the downward direction. Thus, the gravitational intensity at an arbitrary point P of the hemispherical shell has the direction as indicated by arrow e

Therefore the correct option is(B): e.