If gravitational attraction between two points masses be given by `F=G(m_(1)m_(2))/(r^(n))`. Then the period of a satellite in a circular orbit will be proportional to

Options

A. r
B. `r^(2)`
C. `r^((1)/(2))`
D. independent of `n`

Answer

B

Explanation

`(mv^(2))/(r)=(Gm_(1)m_(2))/(r^(3))or v prop r^(((1-3)/(2)))`
Now, `T=(2pir)/(v)or T prop (r)/(v)`
`:. T prop(r)/(._(r)((1-3)/(2)))rArr T prop r^((1-3)/(2))=r^(2)`.