Question

Two particles A and B move in concentric circles with radii in the ratio \(2:1\). If for every completion of one circle of A, B completes 5 circles, then the ratio of their respective orbital velocities is

• A. \(1:1\)
• B. \(1:2\)
• C. \(2:5\)
• D. \(5:2\)
• E. \(1:5\)

Hint:

\(v = \frac{2\pi r}{T} = 2\pi r f\). Velocity ratio = (radius ratio) × (frequency ratio).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Orbital velocity \(v = \frac{2\pi r}{T}\). Given \(r_A : r_B = 2:1\) and frequency ratio \(f_A : f_B = 1:5\), so \(T_A : T_B = 5:1\).

Step 2: Detailed Explanation:
\(\frac{v_A}{v_B} = \frac{r_A/T_A}{r_B/T_B} = \frac{r_A}{r_B} \times \frac{T_B}{T_A} = \frac{2}{1} \times \frac{1}{5} = \frac{2}{5}\)
Ratio \(v_A : v_B = 2:5\)

Step 3: Final Answer:
The ratio of orbital velocities is \(2:5\).