Two cars of masses ' $\mathrm{m}_{1}$ ', and ' $\mathrm{m}_{2}$ ' are moving in the circles of radii '…
Two cars of masses ' $\mathrm{m}_{1}$ ', and ' $\mathrm{m}_{2}$ ' are moving in the circles of radii ' $\mathrm{r}_{1}$ ' and ' $\mathrm{r}_{2}$ '
respectively. Their angular speeds ' $\omega_{1}$ ' and ' $\omega_{2}$ ' are such that they both complete one revolution in the same time ' $\mathrm{t}^{\prime}$. The ratio of linear speed of ' $\mathrm{m}_{1}$ ' to the linear
speed of ' $\mathrm{m}_{2}$ ' is
$\mathrm{r}_{1}: \mathrm{r}_{2}$
$\mathrm{~T}_{1}^{2}: \mathrm{T}_{2}^{2}$
$\omega_{1}^{2}: \omega_{2}^{2}$
$\mathrm{~m}_{1}: \mathrm{m}_{2}$
Solution
They complete one revolution in the same time.
$\begin{array}{l}
\therefore \omega_{1}=\omega_{2} \\
\therefore \frac{V_{1}}{r_{1}}=\frac{V_{2}}{r_{2}} \\
\therefore \frac{V_{1}}{V_{2}}=\frac{r_{1}}{r_{2}}
\end{array}$
^