question_answer

Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between the sun and planet i.e.   \[{{T}^{2}}=K{{r}^{3}},\] here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitation force of attraction between them is\[F=\frac{GMm}{{{r}^{2}}},\] here G is gravitational constant. The relation between G and K is described as [NEET 2015 ]

A) \[GK=4{{\pi }^{2}}\]

B) \[GMK=4{{\pi }^{2}}\]

C) \[K=G\]

D) \[K=\frac{l}{G}\]

Correct Answer: B

Solution :

The gravitational force of attraction between the planet and sun provide the centripetal force

i.e.

The time period of planet will be

(i)

Also from Kepler's third law

(ii)

From Eqs. (i) and (ii), we get