Suppose the gravitational force varies inversely as the `n^(th)` power of distance. Then the time period of a planet in circular orbit of radius `r` around the sun will be proportional to

Options

A. `R^((n+1)//2)`
B. `R^((n-1)//2)`
C. `R^n`
D. `R^((n-1)//2)`

Answer

A

Explanation

`mw^2R prop 1/R^n rArr m((4pi^2)/T^2)R prop 1/R^n rArr T^2 prop R^(n+1) therefore T prop R^((n+1)/2)`