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Q. No.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: Â Banking of Roads |
 88%
Level 1: 80%+
NEET - 2016
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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: Â Banking of Roads |
 89%
Level 1: 80%+
AIPMT - 2012
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The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1.
2.
3.
4.
Subtopic: Â Banking of Roads |
 86%
Level 1: 80%+
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Given below are two statements:
| Assertion (A): | Improper banking of roads causes wear and tear of tyres. |
| Reason (R): | The necessary centripetal force in that event is provided by the force of friction between the tyres and the road. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Â Banking of Roads |
 70%
Level 2: 60%+
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A car is moving on a circular track of radius \(50~\text{cm}\) with coefficient of friction being \(0.34.\) On this horizontal track, the maximum safe speed for turning is equal to:
(take \(g=10~\text{m/s}^2\) )
1. \(1.03~\text{m/s}\)
2. \(1.7~\text{m/s}\)
3. \(1.3~\text{m/s}\)
4. \(1.8~\text{m/s}\)
(take \(g=10~\text{m/s}^2\) )
1. \(1.03~\text{m/s}\)
2. \(1.7~\text{m/s}\)
3. \(1.3~\text{m/s}\)
4. \(1.8~\text{m/s}\)
Subtopic: Â Banking of Roads |
 62%
Level 2: 60%+
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