Gravitation

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Question : 10
Total: 25
The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see figure) (i) a, (ii) b, (iii) c, (iv) 0.
Solution:  
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 Q 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.
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