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Angular Velocity

Two cars c1...

Question

Two cars $c_{1}$ and $c_{2}$ are going round concentric circles of radii $r_{1}$ and $r_{2}$ . They complete the circular paths in the same time then $\frac{s p e e d o f c_{1}}{s p e e d o f c_{2}}$ :

r_{2} / r_{1}

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r_{1} / r_{2}

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none of these

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Solution

The correct option is B $r_{1} / r_{2}$
We have
$t_{1} = \frac{2 π r_{1}}{v_{1}} t_{2} = \frac{2 π r_{2}}{v_{2}}$
$∵ t_{1} = t_{2} \Rightarrow \frac{2 π r_{1}}{v_{1}} = \frac{2 π r_{2}}{v_{2}} \Rightarrow \frac{v_{1}}{v_{2}} = \frac{r_{1}}{r_{2}}$
$\Rightarrow \frac{speed of c_{1}}{speed of c_{2}} = \frac{r_{1}}{r_{2}}$

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