Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii $r_{A

Question

Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii $r_{A}$ and $r_{B}$ respectively. Their time period of rotation is the same. The ratio of the linear speed of $A$ to that of $B$ will be

Professor PC Thomas Classes · Answer

(b) : Time period, $T=\frac{2 \pi}{\omega}$. As $T_{A}=T_{B}$, $\omega_{A} = \omega_{B}$. \ Linear speed $v = r\omega$. \ $	herefore \frac{v_{A}}{v_{B}} = \frac{r_{A} \omega_{A}}{r_{B} \omega_{B}} = \frac{r_{A}}{r_{B}}$