A solid sphere of uniform density and radius 4 units is located w… - Vidyadip

MCQ

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
The gravitational force due to this object at the origin is zero
B
The gravitational potential is the same at all points on the circle ${y^2} + {z^2} = 4$
C
The gravitational potential is the same at all points of the circle ${y^2} + {z^2} = 36$
✓
All of the above

✓

Answer

Correct option: D.

All of the above

d
(d) 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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