The distance of two satellites from the surface of the earth `R` and `7R`. There time periods of rotation are in the ratio

Options

A. `1:7`
B. `1:8`
C. `1:49`
D. `1:7^(3//2)`

Answer

B

Explanation

`T^(2) prop r^(3) implies T^(2) prop (R+h)^(3)`
`(T_(1))/(T_(2))=((R+h_(1))/(R+h_(2)))^(3//2)=((R+R)/(R+7R))^(3//2)=(1/4)^(3//2)`
`=1/4(1/4)^(1//2)=1/8`