A satellite is seen every `6 h` over the equator. It is known that it rotates opposite to that of earth's direction. Then, the angular velocity (in radius per hour) of satellite about the centre of earth will be

Options

A. `pi/2`
B. `pi/3`
C. `pi/4`
D. `pi/8`

Answer

C

Explanation

Let `omega_(E)`=angular velocity of earth, `omega_(S)` =angular velocity of satellite.
Then `6=(2pi)/((omega_(E)+omega_(S)) implies omega_(E)+omega_(S)=pi/3`
`implies omega_(S)=(pi)/3-(pi)/(12) ( :. omega_(E)=(2pi)/24=pi/12` rad per hour)
`omega_(S)=pi/4` radian per hour