Question

Two particles A and B move in concentric circles of radii \(r_{1}\) and \(r_{2}\) respectively in such a way that position of particles A, B and the centre of the circle (O) always lie on a straight line, the ratio of their angular velocities (\(\omega _{1}:\omega _{2}\)) is

• A. \(r_{1}:r_{2}\)
• B. \(r_{2}:r_{1}\)
• C. \(1:2\)
• D. \(1:1\)

Hint:

If the two particles and the centre always stay on one straight line, they sweep equal angles in equal times.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Angular velocity is the angle swept per unit time, \(\omega=\dfrac{\Delta\theta}{\Delta t}\).

Step 2: Using the condition
O, A and B always lie on one straight line. The line OAB turns as a rigid line, so both particles sweep the same angle in the same time.

Step 3: Result
\(\omega_{1}=\omega_{2}\), so \(\omega_{1}:\omega_{2}=1:1\). Only the linear speeds differ, \(v_{1}:v_{2}=r_{1}:r_{2}\).

Final Answer:
The ratio of their angular velocities is 1:1. \[ \boxed{\text{(D) }1:1} \]