Question

Two particles having mass 'M' and 'm' are moving in a circular path with radius 'R' and 'r' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to that of the second particle will be

• A. \(1:1\)
• B. \(1:2\)
• C. \(2:3\)
• D. \(3:4\)

Hint:

Angular velocity depends only on the time period, not on mass or radius.

Answer 1

The Correct Option is A

Step 1: Definition:
Angular velocity is the angle swept per unit time. One full turn $2\pi$ takes the period $T$.

Step 2: Compare:
Same $T$ means the same angle per second for both particles, whatever their radii or masses.

Step 3: Answer:
Ratio $1:1$, option (A). The linear speeds differ ($v=\omega R$), but the angular velocities are equal.

Final Answer:
Option (A). \[ \boxed{\text{(A) } 1:1} \]