The ratio of mean distances of three planets from the sun are `0.5 : 1: 1:5`, then the square of time periods are in the ratio of

Options

A. `1:4:9`
B. `1:9:4`
C. `1:8:27`
D. `2:1:3`

Answer

C

Explanation

According to Kepler's third law,
`T^(2)prop r^(3),r_(1):r_(2):r_(3)=(1)/(2):1:(3)/(2)`
`:. T_(1)^(2):T_(2)^(2):T_(3)^(2)=(1)/(8):1:(27)/(8)=1:8:27`