GravitationHard
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 shown in figure.
Options
A.the gravitiational field at the point B (2, 0, 0) is zero
B.the gravitational field due to this object at the origin is zero
C.the gravitational potential is the same at all points of circle y2 + z2 = 36
D.the gravitiational potential is the same at all point s on the circle y2 + z2 = 4
Solution
(a) The gravitational field is zero at the centre of a solid sphere. The samll 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.
(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 to the positive mass M and negative masses - m and - m.
(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 to the positive mass M and negative masses - m and - m.
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