question_answer 10)

The gravitational intensity at the centre Q of                         the drumhead defined by a hemispherical shell of uniform mass density has the direction           indicated by the arrow (6(NCT).l), (i) a, (ii) b ,  (iii) c, (iv) zero.              

Answer:

We know that 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,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 hemispherical 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.