The time period of `a` satellite of earth is `8` hours. If the separation between the earth and the satellite is increased to two times the previous value, find the new time period of the satellite.

Options

A. `16 sqrt(2)h`
B. `8h`
C. `16h`
D. `10h`

Answer

A

Explanation

Here, `T_(1) = 8 h`, `r_(1) = r` radius of the orbit of satellite.
`T_(2) = ?`, when, `r_(2) = 2 r`
As `(T_(2)^(2))/(T_(1)^(2)) = (r_(2)^(3))/(r_(1)^(3))` or `T_(2) = T_(1)(r_(2)/(r_(1)))^(3//2)`
`= 8((2r)/(r))^(3//2) = 16 sqrt(2) h`