- 1(current)
Q. No.A car travels on a circular racetrack of radius \(50\) m, which is banked at an angle \(\theta\). If the car travels at a speed \(10\) ms\(^{-1}\), then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be \(10\) ms\(^{-2}\), the value of \(\theta\) is:
1. \(\tan^{-1}(2\sqrt{3})~\)
2. \(\tan^{-1}\left(\dfrac{1}{5}\right)~\)
3. \(\tan^{-1}\left(\dfrac{2}{5}\right)~\)
4. \(\tan^{-1}(\sqrt{3}/2)~\)
1. \(\tan^{-1}(2\sqrt{3})~\)
2. \(\tan^{-1}\left(\dfrac{1}{5}\right)~\)
3. \(\tan^{-1}\left(\dfrac{2}{5}\right)~\)
4. \(\tan^{-1}(\sqrt{3}/2)~\)
Subtopic: Banking of Roads |
80%
Level 1: 80%+
NEET - 2026
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A car is negotiating a curved road of radius \(R\). The road is banked at an angle \(\theta\). The coefficient of friction between the tyre of the car and the road is \(\mu_s\). The maximum safe velocity on this road is:
| 1. | \(\sqrt{\operatorname{gR}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\) | 2. | \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\) |
| 3. | \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}^2}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\operatorname{s}} \tan \theta}\right)}\) | 4. | \(\sqrt{\mathrm{gR}^2\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\) |
Subtopic: Banking of Roads |
88%
Level 1: 80%+
NEET - 2016
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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 of \(45^\circ,\) the speed of the car is:
| 1. | \(20\) ms–1 | 2. | \(30\) ms–1 |
| 3. | \(5\) ms–1 | 4. | \(10\) ms–1 |
Subtopic: Banking of Roads |
90%
Level 1: 80%+
AIPMT - 2012
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A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:
| 1. | \(\sqrt{\dfrac{Rg}{\mu_s} }\) | 2. | \(\sqrt{\dfrac{mRg}{\mu_s}}\) |
| 3. | \(\sqrt{\mu_s Rg}\) | 4. | \(\sqrt{\mu_s m Rg}\) |
Subtopic: Banking of Roads |
88%
Level 1: 80%+
AIPMT - 2012
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