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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 complete one revolution in the same time \(t\). The ratio of their centripetal accelerations is:

1. \(m_1 r_1 : m_2 r_2\)
2. \(m_1 : m_2\)
3. \(r_1 : r_2\)
4. 1 : 1

Correct answer: \(r_1 : r_2\)

Solution

Since both cars complete one revolution in the same time, they have the same time period. Centripetal acceleration is \(a_c = 4\pi^2 r/T^2\), so it is directly proportional to radius when \(T\) is the same.

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