Two planets revolve round the sun with frequencies `N_(1)` and `N_(2)` revolutions per year. If their average orbital radii be `R_(1)` and `R_(2)` respectively, then `R_(1)//R_(2)` is equal to

Options

A. `(N_(1)//N_(2))^(3//2)`
B. `(N_(2)//N_(1))^(3//2)`
C. `(N_(1)//N_(2))^(2//3)`
D. `(N_(2)//N_(1))^(2//3)`

Answer

d

Explanation

`Tprop R^(3//2)" as "T_(1)=(1)/(N_(1))`
`therefore" "(1)/(N_(1)) prop R_(1)^(3//2)" and ""(1)/(N_(2)) prop R_(2)^(3//2)`
`(N_(2))/(N_(1))=((R_(1))/(R_(2)))^(3//2) or (R_(1))/(R_(2))=((N_(2))/(N_(1)))^(2//3)`