A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R³. Its time period of revolution will be given by

Question

Accepted Answer

(2) T∝ R². Idea: set the given force law equal to the centripetal requirement written in terms of the period, then compare powers of R. The centripetal force is F=mω²R=m((2π)/T)²R=(4π²mR)/(T²). Setting this proportional to R⁻³: R/(T²)∝1/(R³) T²∝ R⁴, so T∝ R². The general rule is worth carrying: for F∝ Rⁿ, T²∝ R¹⁻ⁿ. With n=-2 that gives Kepler's T²∝ R³; with n=-3 it gives T²∝ R⁴, as here.

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R³. Its time period of revolution will be given by

Step-by-step solution

Why the other options are wrong