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 $(2,0,0)$ respectively are taken out of the solid leaving behind spherical cavities as shown in figure

• A. The gravitational potential is the same at all points on the circle $y^2+z^2=4$
• B. The gravitational force due to this object at the origin is zero
• C. The gravitational force at the point $B(2,0,0)$ is zero
• D. The gravitational potential is the same at all points of the circle $y^2+z^2=36$

Answer 1

Answer: (A), (B), (D)

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

Since cavities are symmetrical with respect to O. So the gravitational force at the centre is zero.
The radius of the circle $z^2+y^2=36$ 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 $z^2+y^2=4$ as well