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Standard XII

Physics

Uniform Circular Motion

Two cars C 1 ...

Question

Two cars $c_{1}$ and $c_{2}$ are going around in concentric circles of radii $r_{1}$ and $r_{2}$ . They complete the circular paths in the same time. Then, the ratio of speed of $c_{1}$ to speed of $c_{2}$ is

\frac{r_{2}}{r_{1}}

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\frac{r_{1}}{r_{2}}

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Solution

The correct option is B $\frac{r_{1}}{r_{2}}$
Given the time periods are same.
i.e $T_{1} = T_{2}$
$\Rightarrow \frac{2 π}{ω_{1}} = \frac{2 π}{ω_{2}}$
$\Rightarrow ω_{1} = ω_{2}$
Therefore, ratio of speeds $\frac{v_{1}}{v_{2}} = \frac{ω_{1} r_{1}}{ω_{2} r_{2}} = \frac{r_{1}}{r_{2}}$

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The correct option is B $\frac{r_{1}}{r_{2}}$
Given the time periods are same.
i.e $T_{1} = T_{2}$
$\Rightarrow \frac{2 π}{ω_{1}} = \frac{2 π}{ω_{2}}$
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Therefore, ratio of speeds $\frac{v_{1}}{v_{2}} = \frac{ω_{1} r_{1}}{ω_{2} r_{2}} = \frac{r_{1}}{r_{2}}$