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 times the distance of `B` from the sun

Options

A. 5
B. 4
C. 3
D. 2

Answer

B

Explanation

According to Kepler's third law, `T^(2) prop r^(3)`
`because T_(A)=8T_(B)rArr (T_(A))/(T_(B))=(8)/(1)`
`rArr ((T_(A))/(T_(B)))^(2)=((r_(A))/(r_(B)))^(3)rArr((8)/(1))^(2)=((r_(A))/(r_(B)))^(3)rArr(r_(A))/(r_(B))=4`
`rArr r_(A)= 4 r_(B)`.