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

Options

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

Answer

A

Explanation

`F prop 1/(R^(n)) implies F=k/(R^(n))`
`F=(mv^(2))/R`
`k/(R^(n))=(mv^(2))/Rimplies v^(2) prop 1/(R^(n-1)) implies v prop 1/(R^((n+1)/2))`
`T=(2piR)/v implies T prop R/v`
`T prop R.R^((n+1)/2)implies T prop R^((n+1)/2)`