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
  1. $\mathrm{r}_{1}: \mathrm{r}_{2}$
  2. $\mathrm{~T}_{1}^{2}: \mathrm{T}_{2}^{2}$
  3. $\omega_{1}^{2}: \omega_{2}^{2}$
  4. $\mathrm{~m}_{1}: \mathrm{m}_{2}$

Solution

They complete one revolution in the same time. $\begin{array}{l} \therefore \omega_{1}=\omega_{2} \\ \therefore \frac{V_{1}}{r_{1}}=\frac{V_{2}}{r_{2}} \\ \therefore \frac{V_{1}}{V_{2}}=\frac{r_{1}}{r_{2}} \end{array}$ ^

Asked in: MHT CET 2020 (12 Oct Shift 1)

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