Question

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

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{8}$

Answer 1

The correct option is C $\frac{\pi }{4}$

Let $w_1$ and $w_2$ be the angular speed of the satellite and earth respectively.

Angular speed of rotation of earth $w_2=\frac{2\pi }{24}$ $rad/hr$

Since, both are revolving in opposite direction. Thus sum of angle rotated by them in time $t=6$ hr is $2\pi$.

$\therefore$ ${\omega }_{1}t+{\omega }_{2}t=2\pi$

$\left({\omega }_1\right)6+\left(\frac{2\pi }{24}\right)6=2\pi$

or $6{\omega }_1=\frac{3\pi }{2}$

$⟹{\omega }_1=\left(\frac{\pi }{4}\right)\frac{rad}{hr}$