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 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 force due to this object at the origin is zero

Answer 1

Answer: (A), (C), (D)

The gravitational force due to this object at the origin is zero

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