The distance of Neptune and Saturn from the sun is nearly `10^(13)m " and "10^(12)m` respectively. Assuming that they move in circular orbits, then what will be the ratio of their time periods.

Options

A. 10
B. 100
C. `10sqrt10`
D. 1000

Answer

C

Explanation

Using Kepler.s Third law of gravitation, we get
`(T _(n) ^(2))/( T _(s) ^(2)) = (R _(n) ^(3))/( R _(s) ^(3)) `
`(T_(n))/( T _(s)) = [ (10 ^(13))/( 10 ^(12)]]^( 3//2)`
`= (sqrt10) ^(3) = 10 sqrt10`