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(D) The centripetal acceleration $a_c$ of an object moving in a circle is given by $a_c = \omega^2 r$,where $\omega$ is the angular velocity and $r$ i

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$r_1 : r_2$

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(D) The centripetal acceleration $a_c$ of an object moving in a circle is given by $a_c = \omega^2 r$,where $\omega$ is the angular velocity and $r$ is the radius of the circle.Since both cars complete their circles in the same time $t$,their angular velocities are equal,given by $\omega = \frac{2\pi}{t}$.Let $a_1$ and $a_2$ be the centripetal accelerations of the two cars respectively.Then,$a_1 = \omega^2 r_1$ and $a_2 = \omega^2 r_2$.The ratio of their centripetal acceleration is $\frac{a_1}{a_2} = \frac{\omega^2 r_1}{\omega^2 r_2} = \frac{r_1}{r_2}$.Thus,the ratio is $r_1 : r_2$.

Two 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 make complete circles in the same time $t$. The ratio of their centripetal acceleration is

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