Two satellites `S_(1)` and `S_(2)` revolve around a planet in coplanar circular orbits in the same sense their periods of revolution are 1 hour and 8hours respectively the radius of the orbit of `S_(1)` is `10^(4)` km when `S_(1)` is closest to `S_(2)` the angular speed of `S_(2)` as observed by an astronaut in `S_(1)` is :

Options

A. `pirad//hr`
B. `pi//3 rad//hr`
C. `2pirad//hr`
D. `pi//2rad//hr`

Answer

B

Explanation

`omega_(1)=(2pi)/1rad//hr`
`omega_(2)=(2pi)/8rad//hr`
`(T_(1)/T_(2))^(2)= (R_(1)/R_(3))^(3)Rightarrow R_(2)/R_(1)=4 RightarrowR_(2)=4xx10^(4)km`
`V_(1)=(2piR)_(1)/1h=2pixx10^(4)km//hr V_(2)=(2piR_(2))/(8h)=pixx10^(4)km//hr`
at closest separation `omega=(V_(rel)bot to line joining)/(length of line journing) =(pixx10^(4)km//hr)/(3xx10^(4)km) = pi/3rad//hr`