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 poitns of the circle `y^(2)+z^(2)=36`
D. the gravitational potential is the same at all points of the circle `y^(2)+z^(2)=4`

Answer

A, C, D

Explanation

(A) Net gravitational field at centre due to solid sphere (having cavites) is equal to zero.
let point P is in y-z plane (o,y,z) then equipotential curve must be circle y-z plane `bot^(2)` to the diameter passing through eavities.