Two objects of masses ' $m_1$ ' and ' $m_2$ ' are moving in the circles of radii ' $r_1$ ' and ' $r_2$ '…
Two objects of masses ' $m_1$ ' and ' $m_2$ ' are moving in the circles of radii ' $r_1$ ' and ' $r_2$ ' respectively. Their respective angular speeds ' $\omega_1$ ' and ' $\omega_2$ ' are such that they both complete one revolution in the same time ' $t$ '. The ratio of linear speed of ' $\mathrm{m}_2$ ' to that of ' $\mathrm{m}_1$ ' is
$\omega_1: \omega_2$
$\mathrm{T}_2: \mathrm{T}_1$
$\mathrm{m}_1: \mathrm{m}_2$
$\mathrm{r}_2: \mathrm{r}_1$
Solution
The cars complete one revolution in the same time.
$\begin{array}{ll}
\therefore & \omega_1=\omega_2 \\
\therefore & \frac{\mathrm{v}_1}{\mathrm{r}_1}=\frac{\mathrm{v}_2}{\mathrm{r}_2} \Rightarrow \frac{\mathrm{v}_2}{\mathrm{v}_1}=\frac{\mathrm{r}_2}{\mathrm{r}_1}
\end{array}$
^