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-2)/(2)))`

Answer

A

Explanation

`F=(GMm)/(r^(n))=momega^(2)r`
`impliesomega=sqrt((GM)/(r^(n+1)))impliesT=(2pi)/(omega)=(r^((n+1)/(2)))`