Questions

Suppose the gravitational force varies inversely as the $n^{t h}$ power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to

Remember concepts with our Masterclasses.

80k Users

60 mins Expert Faculty Ask Questions

Rn+12

Rn−12

Rn−22

Ready to Test Your Skills?

Check Your Performance Today with our Free Mock Tests used by Toppers!

detailed solution

Correct option is A

F∝1Rn----(1) ⇒Gravitational force provides centripetal force⇒F=mω2R---(2) From equations (1) and(2) we get ⇒mω2R∝1Rn⇒m4π2T2R∝1Rn∵ω=2πT ⇒1T2R∝1Rn∵m,4,π are constants ⇒RnR∝T2⇒T2∝Rn+1 ∴T∝Rn+12

Talk to our academic expert!

Create Your Own Test
Your Topic, Your Difficulty, Your Pace

Similar Questions

In the following four periods
(i) Time of revolution of a satellite just above the earth’s surface $(T_{s t})$
(ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth $(T_{m a})$
(iii) Period of simple pendulum having a length equal to the earth’s radius in a uniform field of 9.8 N/kg $(T_{s p})$
(iv) Period of an infinite length simple pendulum in the earth’s real gravitational field $(T_{i s})$