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

(b) 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