Suppose the gravitational force varies inversely as then n th power of distance then the time period of a planet in circular orbit of radius r around the sun will be propotinal to

Options

A. `r^(1/2(n+1))`
B. `r^(1/2(n-1))`
C. `(2R)/(3)`
D. `R`

Answer

A

Explanation

`(mv^(2))/(r ) prop r^(-n)` or `v prop r^(1-n)//2`
`rarr T=(2pir)/(v)`
`T prop rv^(-1)` or `T prop r.r^(n-1)//2`
`rarr T prop r^(n+1)//2`