- 1(current)
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. \(\sqrt{\mathrm{gR}^2\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1.
2.
3.
4.
| 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. |
(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. \(1.8~\text{m/s}\)
- 1(current)
Q. No.
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