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A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is \(45^\circ\), the speed of the car is:

1. 20 m s\(^{-1}\)
2. 30 m s\(^{-1}\)
3. 5 m s\(^{-1}\)
4. 10 m s\(^{-1}\)

Correct answer: 30 m s\(^{-1}\)

Solution

On a frictionless banked curve, the horizontal component of normal reaction provides centripetal force, giving \(v^2 = rg\tan\theta\). Substituting \(r=90\,\text{m}\) and \(\theta=45^\circ\) gives \(v \approx 30\,\text{m/s}\).

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