​ The mass density of a spherical galaxy varies as k/r over a large distance ‘r’ from its centre. ​

Question

The mass density of a spherical galaxy varies as \(\frac{k}{r}\) over a large distance ‘r’ from its centre. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as

(1)  T² ∝ \(\frac{1}{R^3}\)

(2)  T² ∝ R

(3)  T ∝ R

(4)  T² ∝ R³

Answer 1

Answer is (2) T² ∝ R