System Of Particles And Rotational Motion Ques 10

10. Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii $r_A$ and $r_B$ with speed $v_A$ 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 :

[2019]

(a) $r_A: r_B$

(b) $v_A: v_B$

(c) $r_B: r_A$

(d) $1: 1$

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Answer:

Correct Answer: 10.(d)

Solution:

  1. (d) Let $T_A$ and $T_B$ are the time periods of particle $A$ and $B$ respectively. According to question,

$T_A=T_B=T$

If $\omega_A$ and $\omega_B$ are their angular speeds, then

$\omega_A=\frac{2 \pi}{T_A}$ and $\omega_B=\frac{2 \pi}{T_B}$

$ \therefore \frac{\omega_A}{\omega_B}=\frac{T_B}{T A}=\frac{T}{T}=1: 1 $

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