Two cars of masses $m_{1}$ and $m_{2}$ are moving along the circular paths of radius $r_{1}$ and $r_{2}$ respectively. The speeds are such that they complete one round at the same time. The ratio of angular speeds of two cars is

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
Angular velocity is the rate of change of angular displacement with time.

Given that the cars complete one circle in the same time $t$ .

$A n g u l a r s p e e d, ω = \frac{A n g l e s u b t e n d e d b y t h e c a r f o r o n e r e v o l u t i o n (2 π)}{T i m e t a k e n (t)}$

Angular speed of first car, $ω_{1} = \frac{2 π}{t}$

Angular speed of second car, $ω_{2} = \frac{2 π}{t}$

Therefore, the ratio of angular speed of first car to the second car, $\frac{ω_{1}}{ω_{2}} = \frac{2 π / t}{2 π / t} = \frac{1}{1}$

So, the ratio of angular speed of firts car to the second car is $1 : 1$

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