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Two particles A and B are moving in uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speeds \(v_A\) and \(v_B\), respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be:

1. 1 : 1
2. \(r_A : r_B\)
3. \(v_A : v_B\)
4. \(r_B : r_A\)

Correct answer: 1 : 1

Solution

For uniform circular motion, angular speed is \(\omega = 2\pi/T\). Since both particles have the same time period, their angular speeds are equal, so the ratio is 1:1.

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