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

A

Explanation

Accroding to kepler s third law
`T^(2) prop r^(3) , r_(1),r_(2),r_(3)=1/2:1:3/2`
`therefore T_(1)^(2),T_(2)^(2):T_(3)^(2)=1/8:1:27/8=1:8:27`