Two cars of masses m_{1} and m_{2} are moving | vedclass

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(A) The linear speed $V$ of an object in circular motion is given by $V = r\omega$,where $r$ is the radius and $\omega$ is the angular speed.Since bot

Vedclass · Accepted Answer

$r_{1}: r_{2}$

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(A) The linear speed $V$ of an object in circular motion is given by $V = r\omega$,where $r$ is the radius and $\omega$ is the angular speed.Since both cars complete one revolution in the same time $t$,their angular speeds are equal,i.e.,$\omega_{1} = \omega_{2} = \frac{2\pi}{t}$.Therefore,the ratio of their linear speeds is:$\frac{V_{1}}{V_{2}} = \frac{r_{1}\omega_{1}}{r_{2}\omega_{2}}$Since $\omega_{1} = \omega_{2}$,the ratio simplifies to:$\frac{V_{1}}{V_{2}} = \frac{r_{1}}{r_{2}}$Thus,the ratio of the linear speed of $m_{1}$ to the linear speed of $m_{2}$ 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 angular speeds $\omega_{1}$ and $\omega_{2}$ are such that they both complete one revolution in the same time $t$. The ratio of the linear speed of $m_{1}$ to the linear speed of $m_{2}$ is:

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