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)`
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)`
`:. T=(2piR)/(sqrt(2GM//R^(n-1)))=(2pi)/(sqrt(2GM))xxR^((n+1)//2)`
`T prop R^((n+1)//2)`