Explanation
At the centre of a solid sphere, the gravitational field is zero. The small spheres removed from the big sphere 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 is zero. Thus option (a) is correct. Since the plane of circles is y-z plane, so options (b) and (c) are correct as potential at any point on these two circles will be equal due to positive mass M and negative mass – m at A and –m at B.
Speed of the earth will be maximum when its distance from the sun is minimum because mvr = Constant
During path DAB planet is nearer to sun as comparison with path BCD. So, time taken in travelling DAB is less than that for BCD because velocity of planet will be more in region DAB.
Since cavities are symmetrical w.r.t. O. So, the gravitational force at the centre is zero. The radius of the circle z2 + y2 + 36 is 6. For all point for r ≥ 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 z2 + y2 = 4 as well.
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