Two cars $A$ and $B$ are going around concentric circular paths of radii $R_A$ and $R_B$. If the two cars…
Two cars $A$ and $B$ are going around concentric circular paths of radii $R_A$ and $R_B$. If the two cars complete the circular paths in the same time, then the ratio of angular speed of $A$ and $B$ is
$1: 1$
$R_A: R_B$
$R_B: R_A$
$1: 2$
Solution
Angular speed of a body moving on circular path is given as
$
\omega=\frac{2 \pi}{T}
$
where, $T$ is the time-period.
$\therefore \quad \frac{\omega_A}{\omega_B}=\frac{T_B}{T_A}$
Given, $\quad T_A=T_B$
$\therefore \quad \frac{\omega_A}{\omega_B}=\frac{T_A}{T_A} \Rightarrow \frac{\omega_A}{\omega_B}=\frac{1}{1}$
$\therefore \quad \omega_A: \omega_B=1: 1$