Question

Choose the correct answer from among the given ones:

The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12)
(i) a,
(ii) b,
(iii) c,
(iv) O. Question 8.10 Gravitation

Answer 1

Gravitational intensity is equal to negative of the Gravitational potential gradient .
e.g I = -dV/dr
we know, Gravitational potential inside the spherical shell is constant . so, potential gradient inside the spherical shell is zero. So, Gravitational intensity inside the spherical shell will be zero.
This indicates that gravitational forces acting at a point in a spherical shell are symmetric.
If we removed upper hemisphere shell then, Gravitational force acting on particle placed at centre O will be downward .hence, Gravitational force per unit mass ( Gravitational intensity ) will be downward .
Hence , option (iii) C is correct .

Answer 2

Gravitational potential (V) is constant at all points in a spherical shell. Hence, the gravitational potential gradient (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 located at centre O 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 centre O of the given hemispherical shell has the direction as indicated by arrow C.

the coorect answer is (iii) C