Question

Two satellites P and Q go round a planet in circular orbits having radii ' $3R$ ' and ' $R$ ' respectively. If the speed of satellite $P$ is ' $2V$ ', the speed of the satellite $Q$ will be

• A. $2\sqrt{3}V$
• B. $\frac{2V}{\sqrt{3}}$
• C. $\frac{V}{2}$
• D. $\frac{V}{\sqrt{3}}$

Hint:

Satellite speed in circular orbit varies as: \[ v\propto \frac{1}{\sqrt{r}} \] Smaller radius means higher orbital speed.

Answer 1

The Correct Option is A

Concept:
For a satellite in circular orbit: \[ v=\sqrt{\frac{GM}{r}} \] So, \[ v\propto \frac{1}{\sqrt{r}} \] ip

Step 1: Use the ratio of orbital speeds.
For satellite \(P\): \[ r_P=3R,\qquad v_P=2V \] For satellite \(Q\): \[ r_Q=R \] Now, \[ \frac{v_Q}{v_P}=\sqrt{\frac{r_P}{r_Q}} =\sqrt{\frac{3R}{R}}=\sqrt{3} \] ip

Step 2: Find \(v_Q\).
\[ v_Q=\sqrt{3}\,v_P =\sqrt{3}(2V)=2\sqrt{3}V \] ip Hence, the correct answer is:
\[ \boxed{(A)\ 2\sqrt{3}V} \]