A solid sphere of uniform density and radius 4 units is located with its centre at the…

Physics · JEE Advanced · NTA Exams — Gravitation

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.

 
Then:

1. the gravitational force due to this object at the origin is zero.
2. the gravitational force at the point B(2, 0, 0) is zero.
3. the gravitational potential is the same at all points of circle y² + z² = 36 .
4. the gravitational potential is the same at all points on the circle y² + z² = 4 .