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 figure. Then

• 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 circle $y^2+z^2=36$
• D. the gravitational potential is the same at all points on the circle $y^2+z^2=4$

Answer 1

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

The correct options are
A the gravitational force due to this object at the origin is zero
C the gravitational potential is the same at all points of circle $y^2+z^2=36$
D the gravitational potential is the same at all points on the circle $y^2+z^2=4$