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(C) The angular speed $\omega$ of an object moving in a circular path is defined as the rate of change of angular displacement,given by the formula $\

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$1 : 1$

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(C) The angular speed $\omega$ of an object moving in a circular path is defined as the rate of change of angular displacement,given by the formula $\omega = \frac{2\pi}{T}$,where $T$ is the time period taken to complete one full revolution.Since both cars complete one round in the same time $T$,their time periods are equal $(T_1 = T_2 = T)$.Therefore,the angular speed of the first car is $\omega_1 = \frac{2\pi}{T}$ and the angular speed of the second car is $\omega_2 = \frac{2\pi}{T}$.The ratio of their angular speeds is $\frac{\omega_1}{\omega_2} = \frac{2\pi / T}{2\pi / T} = 1$.Thus,the ratio is $1 : 1$.

Two cars of masses $m_1$ and $m_2$ are moving along circular paths of radii $r_1$ and $r_2$ respectively. Their speeds are such that they complete one round in the same time. The ratio of the angular speeds of the two cars is:

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