question_answer

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to                                                 [AIEEE 2004]

A)  \[{{R}^{\left( \frac{n+1}{2} \right)}}\] 

B)       \[{{R}^{\left( \frac{n-1}{2} \right)}}\]

C)  \[{{R}^{n}}\]             

D)       \[{{R}^{\left( \frac{n-2}{2} \right)}}\]

Correct Answer: A

Solution :

[a] The necessary centripetal force required for a planet to move round the sun

= gravitational force exerted on it

i.e.,

Now,