Two cars of masses $m_{1}$ and $m_{2}$ are moving along the circular path of radius $r_{1}$ and $r_{2}$ . They take one round in the same time. The ratio of angular velocities of the two cars will be -

m_{1} : m_{2}

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r_{1} : r_{2}

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1 : 1

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m_{1} r_{1} : m_{2} r_{2}

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Solution

The correct option is C $1 : 1$
Let the time period is $T$ .

The angular speed is given as,

$ω = \frac{v}{r}$

$ω = \frac{(\frac{2 π r}{T})}{r}$

$ω = \frac{2 π}{T}$

The ratio of angular speed is given as,

$\frac{ω_{1}}{ω_{2}} = \frac{T_{2}}{T_{1}}$

$\frac{ω_{1}}{ω_{2}} = \frac{T}{T}$

$\frac{ω_{1}}{ω_{2}} = \frac{1}{1}$

The ratio of angular velocities of the two cars will be $1 : 1$ .

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