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: Key Relation:
For circular motion, \(\omega=\dfrac{2\pi}T\).

Step 2: Apply:
Both particles have the same period \(T\), so \(\omega_1=\dfrac{2\pi}{T}=\omega_2\).

Step 3: Ratio:
\(\omega_1:\omega_2=1:1\). The masses \(M,m\) and radii \(R,r\) do not appear in the formula for angular velocity, so they do not change the ratio.

Step 4: Check the Other Options:
The ratios \(1:2\), \(2:3\) and \(3:4\) would need different periods. Only equal periods give \(1:1\), so (A) is correct.

Final Answer:
The ratio is \(1:1\), option (A). \[ \boxed{\text{(A) } 1:1} \]