Gravitation 2 Question 7
10. 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.
(1993, 2M)
Then,
(a) the gravitational field due to this object at the origin is zero
(b) the gravitational field at the point $B(2,0,0)$ is zero
(c) the gravitational potential is the same at all points of circle $y^{2}+z^{2}=36$
(d) the gravitational potential is the same at all points on the circle $y^{2}+z^{2}=4$
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Answer:
Correct Answer: 10. (a, c, d)
Solution:
- The gravitational field is zero at the centre of a solid sphere. The small spheres can be considered as negative mass $m$ located at $A$ and $B$. The gravitational field due to these masses at $O$ is equal and opposite. Hence, the resultant field at $O$ is zero, options c and $\mathrm{d}$ are correct because plane of these circles is $y-z$, i.e. perpendicular to $X$-axis i.e. potential at any point on these two circles will be equal due to the positive mass $M$ and negative masses $-m$ and $-m$.
