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 field at distance `r_(1)` and `r_(2)` from the centre of a uniform sphere of radius R and mass `M` are `F_(1)` and `F_(2)` respectively then
B. The gravitational field at the point B(2,0,0) is zero
C. the gravitational potential is the same at all points of circle `y^(2)+z^(2)=36`
D. The gravitational potential is the same at all points on the circle `y^(2)+z^(2)=4`

Answer

A, C, D

Explanation

Due to symmetry the gravitational field at the origin is zero. The equipotential line will take the shape of a circle in yz plane.