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

A $r_A:r_B$

B $v_A:v_B$

C $r_B:r_A$

D $1:1$

The answer is D.

Solution

Given $T_A=T_B=T$. $\omega_A=\frac{2\pi}{T_A}$, $\omega_B=\frac{2\pi}{T_B}$ $\frac{\omega_A}{\omega_B}=\frac{T_B}{T_A}=\frac{T}{T}=1$ Ratio $=1:1$

Concept angular speed for equal time periods

56 questions from this chapter have appeared across 22 exam years.