Question

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 of the solid leaving behind spherical cavities as shown in figure. Then,

• 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 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

Answer: (A), (B), (C)

The gravitational potential is the same at all points of the circle $y^2+z^2=36$

Since cavities are symmetrical w.r.t. O. So the gravitational force at the centre is zero.
The radius of the circle $x^2+y^2=36$ is 6.
For all points for $r\ge 6$, the body behaves as if whole of the mass is concentrated at the centre. So the gravitational potential is same.
Above is true for $x^2+y^2=4$ as well.