The distances of two satellites from the surface of the Earth are R and 7R. Their 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

As `T^(2)propr^(3)` where r = distance from the centre of the Earth.
`therefore(T_1)/(T_2)=((r_1)/(r_2))^(3//2)`
Here, `r_(1)=2R,r_(2)=8R`
`therefore(T_1)/(T_2)=((2R)/(8R))^(3//2)=(1)/(4^(3//2))=(1)/(8)`