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

Answer

B

Explanation

`T=(2piR)/v`
`E=1/2mv^(2)=(GMm)/(R^(n-1))`
or `v=[(2GM)/R^(n-1)]^(1/2)`
`:. G=(2piR)/sqrt((2GM//R^(n-1)))=(2pi)/sqrt(2GM)xxR^(n+1)^(/2)`
`implies TpropR^((n+1)/2)`