Question

A solid sphere of uniform density and radius 4 units is located with its centre at the origin of coordinates, O. Two spheres of equal radii of 1 unit, with their centres at A(-2, 0, 0) and B(2, 0, 0) respectively, are taken out of the solid sphere, leaving behind spherical cavities as shown in the figure.

(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 y² + z² = 36. 

(d) The gravitational potential is the same at all points on the circle y² + z² = 4.

Answer 1

Correct Answer is: (a, c, & d)

Use arguments of symmetry as the yz plane divides the object symmetrically.