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Centripetal Force

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Question

Two cars having masses $m_{1}$ and $m_{2}$ move in circles of radii $r_{1}$ and $r_{2}$ respectively. If they complete the circle in equal time. What is the ratio of their speeds and centripetal accelerations?

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Solution

$v = 2 π r / T$

$v_{1} / v_{2} = r_{1} / r_{2}$ as T is same for both.

$a = v w$ and $w$ is same for both.

$S o, a_{1} / a_{2} = v_{1} / v_{2} = r_{1} / r_{2}$

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