The time of revolution of planet `A` round the sun is `8` times that of another planet `B`. The distance of planet `A` from the sun is how many `B` from the sun

Options

A. `4 : 1`
B. `1 : 2`
C. `3 : 1`
D. `1 : 4`

Answer

D

Explanation

`T^(2)prop r^(3) " " n_(1)^(2)d_(1)^(3)=n_(2)^(2)d_(2)^(3)" " (because T=(1)/(n))`
`therefore ((n_(1))/(n_(2)))^(2)=((d_(2))/(d_(1)))^(3)=((8)/(1))^(3)`
`therefore (d_(2))/(d_(1))=(2^(3))^(2//3)=4 " " therefore (d_(1))/(d_(2))=(1)/(4)`