Question

Two satellites $S_1$ and $S_2$ revolve around a planet in coplanar circular orbits in the same sense. Their periods of revolution are $1hour$ 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

• A. $\pi rad/hr$
• B. $\frac{7\pi }{8}rad/hr$
• C. 2$\pi rad/hr$
• D. $\frac{\pi }{2}rad/hr$

Answer 1

Answer: (B)

$\frac{7\pi }{8}rad/hr$

Angular velocity $\omega =\frac{2\pi }{T}$
Here$,T=1hr$ for $S_1\to {\omega }_1=2\pi rad/hr$
Similarly for $S_2,{\omega }_2=\frac{2\pi }{8}$
Given that they are rotating in same sense. So, relative angular velocity ${\omega }_{21}={\omega }_2-{\omega }_1=2\pi -\frac{2\pi }{8}=\frac{7\pi }{8}$