Two particles having mass ' $M$ ' and ' $m$ ' are moving in a circular path with radius ' $R$ ' and ' $r$ '…

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 the second particle will be
  1. $1: 1$
  2. $1: 2$
  3. $2: 3$
  4. $3: 4$

Solution

$\begin{aligned} & \quad \mathrm{T}=\frac{2 \pi}{\omega} \\ & \quad \text { Hence, } \mathrm{T}_1=\mathrm{T}_2 \\ & \Rightarrow \omega_1=\omega_2 \\ & \therefore \quad \frac{\omega_1}{\omega_2}=\frac{1}{1}\end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 1)

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