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

Answer

A

Explanation

As gravitational fore provides the necessary centripetal force
`(mv^(2))/(r)prop r^(-n)rArr v prop r^((1-n)//2)rArr T=(2pir)/(v) or T prop rv^(-1)`
or `T prop r.r^((n-1)//2)or Tprop r^((n+1)//2)`.