Two satellites `S_1 and S_2` revole round a planet in coplanar circular orbits in the same sanse. Their periods of revolution are 1 hour and 8 hour respectively. The radius of the orbit of `S_1 is 10^4 km,` When `S_2 is closest to S_1` find
(i) the speed of `S_2 relative to `S_1`
(ii) the angular speed of `S_2` as actually observed by an astronaut is `S_1.`

Options

A. `2pixx10^(4)kmph`
B. `pixx10^(4)kmph`
C. `pi/2xx10^(4)kmph`
D. `pi/3xx10^(4)kmph`

Answer

B

Explanation

By Kepler's `3^(rd)` law, `(T^(2))/(R^(3))`=constant.
`:. (T_(1)^(2))/(R_(2)^(3))=(T_(2)^(2))/(R_(1)^(3))` or `1/((10^(4))^(3))=64/(R_(2)^(3))` or `R_(2)=4xx10^(4)km`
Distance travelled in one revolution, `S_(1)=2piR_(1)=2pixx10^(4)` and `S_(2)=2piR_(2)=2pixx4xx10^(4)`
`v_(1)=(S_(1))/(t_(1))=(2pixx10^(4))/1=2pixx10^(4) kmph`
and `v_(2)=(S_(2))/(t_(2))=(2pixx4xx10^(4))/8=pixx10^(4) kmph`
`:.` Relative velocity
`v_(1)-v_(2)=2pixx10^(4)-pixx10^(4)=2pixx10^(4)kmph`