Average distance of the earth from the sun is `L_(1)`. If one year of the earth=D days, one year of another planet whose average distance from the sun is `L_(2)` will be

Options

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

Answer

B

Explanation

According to Kepler.s third law,
`T^(2) prop r^(3). or " T prop r^(3//2)`
`:. (D.)/(D)=((L_(2))/(L_(1)))^(3//2)" or D.=D((L_(2))/(L_(1))^(3//2))" days"`