Gravitation Question 116
Question: 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 [IIT 1993]
Options:
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 $ [y^{2}+z^{2}=36] $
D) The gravitational potential is the same at all points on the circle $ [y^{2}+z^{2}=4] $
Show Answer
Answer:
Correct Answer: A
Solution:
-
Since cavitiesare 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.
