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A solid sphere of uniform density and radius 4 units is located with its center at the origin O of coordinates. Two spheres of equal radii 1 unit, with their centers 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. 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 circle
the gravitational potential is the same at all points on the circle
Answers (1)
The gravitational field is zero at the center of a solid sphere. The small spheres can be considered as negative mass m located at A and B. The gravitational force due to these masses on a mass at O is equal and opposite, hence the resultant force on mass at O is zero.
(C and 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.
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