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