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 (i) a,(ii)b, (iii) c, (iv) zero.

The gravitational intensity at the centre Q of the drumhead defined by

1.	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 (i) a,(ii)b, (iii) c, (iv) zero.
Answer» Solution :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, `(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 symmetrtically 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 also c.i.e., option (iii) is correct.