A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two sphere of equal radii 1 unit, with their centres at A(-2,0 ,0) and B(2,0,0) respectively, are taken out of the solid leaving behind spherical cavities as shown if fig Then:

Options

A. the gravitational force due to this object at the origin is zero
B. the gravitational force at the point `B(2,0,0)` is zero
C. the gravitational potential is the same at all points of the circle `z^(2)+y^(2)=36`
D. the gravitational potential is same at all points of the cirlcle `y^(2)+z^(2)=4`

Answer

A, C, D

Explanation

The mass of the sphere with cavities is symmetrically situated with respect to the origin. The circle `y^(2)+z^(2)=36` has a radius of `6` units and all points on it are at a distance of `6` units from the centre of the sphere where the whole mass of the sphere is supposed to be concentrated. the cirlce is outside the sphere. similar is the case with circle `y^(2)+z^(2)=4`.