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Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that they each complete one full circle in the same time $t$. The ratio of the angular speed of the first car to the second car is:

1. $m_1 : m_2$
2. $r_1 : r_2$
3. $1 : 1$
4. $m_1 r_1 : m_2 r_2$

Correct answer: $1 : 1$

Solution

Angular speed is given by $\omega = \frac{2\pi}{T}$. Since both cars complete one revolution in the same time $t$, their time periods are equal, so their angular speeds are equal. Hence the ratio is $1:1$.

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