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 in figure
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 in figure
The gravitational force due to this object at the origin is zero
The gravitational potential is the same at all points on the circle ${y^2} + {z^2} = 4$
The gravitational potential is the same at all points of the circle ${y^2} + {z^2} = 36$
All of the above
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 in figure
Since cavities are symmetrical w.r.t. $O$. 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.
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