Question

A solid sphere of uniform density and radius 4 units is located with its centre at the origin O. Two spheres 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 in the figure. Then choose the incorrect statement.

• A. The gravitational force due to this object at the origin is zero.
• B. The gravitational force at point B (2, 0, 0) is zero.
• C. The gravitational potential is the same at all points 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 1

The correct option is B

The gravitational force at point B (2, 0, 0) is zero.

The distance of each cavity from the centre O is the same. Since the two cavities are symmetrical with respect to the centre O, the gravitational force due to the sphere is zero at the centre. Hence, choice (a) is correct.
Regarding potential at a point on the circle $x^2+z^2=36$, we can see that all the points on it are symmetrically located. Hence, potential must be same at every point on this circle. Same logic holds for the circle $y^2+z^2=4$ also. Hence, choices (c) and (d) are correct.
But the gravitational force at point B cannot be zero. Hence, choice (b) is incorrect.