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Mechanics
Easy
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 carvities as shown in the figure., Then
- the gravitational force due to this object at the origin is zero
- the gravitational force at the point B(2,0,0) is zero
- the gravitational potential is the same at all points of the circle
- the gravitational potential is same at all points of the circle
The correct answers are: the gravitational force due to this object at the origin is zero, the gravitational potential is the same at all points of the circle , the gravitational potential is same at all points of the circle
Sol: The mass of the sphere with cavities is symmetrically situated with respect to the origin. The circle 
has a radius of 6 units and all points on it are at a distance of 6 units from the centre of the sphere where the whole mass of the sphere is supposed to be concentrated. The circle is outside the sphere. Similar is the case with circle .
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