In a solid sphere, two small symmetrical cavities are created whose centers lie on a diameter AB of sphere on opposite sides of the centre.

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The gravitational field at the centre of the sphere is zero.

circle at which all points have same potential is in the perpendicular to the diameter AB.

The gravitational potential at the centre remains unaffected if cavities are not present

A circle at which all points have same potential is in the plane of diameter AB.

answer is A, D.

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Detailed Solution

The spherical cavities can be assumed to the negative masses placed symmetrically about origin. So, the gravitational force due to thus object at origin is zero. The circle in perpendicular plane is an equipotential surface (as two cavities are lying symmetrically on each side of equipotential surface), so gravitational potential is same at all the points lying on this circle.

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