Chapter: Rotational Dynamics· Physics

The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec.

Q.24 The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec.

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

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Answer: \(\theta = \tan^{-1}(0.3189) \approx 17^\circ 41'\)

Given: \(r = 200\) m, \(v = 25\) m/s, \(g = 9.8\) m/s\(^2\).

For a banked road (neglecting friction), the horizontal component of the normal reaction provides the centripetal force: \(N\sin\theta = \dfrac{mv^2}{r}\) and \(N\cos\theta = mg\). Dividing,

\(\tan\theta = \dfrac{v^2}{rg} = \dfrac{25^2}{200\times9.8} = \dfrac{625}{1960} = 0.3189\)

\(\theta = \tan^{-1}(0.3189) \approx 17^\circ 41'\) (about 17.7°).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec.

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