# A solid sphere of uniform density and radius 4 units is located with its center at origin O. Two spheres of equal radii/ units with their center $A(-2,0,0)$ and $B(2,0,0)$ respectively are taken out of the solid leaving behind cavities as shown Then

a) The gravitational field due to this object at orgin is zero

b) The gravitational field at B(2,0,0) is zero

c)The gravitational potential is same at all points on the circle. $y^2+z^2=36$

d) The gravitational potential is same at all points on the circle. $y^2+z^2=4$

The gravitational field is zero at center of solid sphere
The small sphere can be considered as $-ve$ masses located at A and B.
The gravitational field due to there masses at 0 is equal and opposite.
Hence resultant field is zero at 0
The planes of circle $y^2+z^2=36$ and $y^2+z^2=4$ is $y-z$
Potential at any point on these circle will be equal due to positive mass M and negative masses m and -m
Hence a is the correct answer.

answered Aug 30, 2013 by
edited Feb 18, 2014 by meena.p