- 1(current)
Q. No.1. \(560\) N
2. \(400\) N
3. \(360\) N
4. \(200\) N
1. \(12\) m/s
2. \(24\) m/s
3. \(32\) m/s
4. \(44\) m/s
A car is moving on a banked road with a radius \(R.\) If \(\theta\) is the banking angle and \(g\) is the acceleration due to gravity, which of the following expressions represents the optimum speed \(v,\) at which the car can navigate the turn without requiring friction?
| 1. | \(v=\sqrt{Rg \mathrm{~tan \theta}}\) | 2. | \(v=\sqrt{Rg \mathrm{~sin \theta}}\) |
| 3. | \(v=\sqrt{Rg \mathrm{~cos \theta}}\) | 4. | \(v=\sqrt{Rg \mathrm{~cot \theta}}\) |
A car is negotiating a curved road of radius \(R.\) The road is banked at angle \(\theta.\) The coefficient of friction between the tyres of the car and the road is \(\mu_s.\) The maximum safe velocity on this road is:
1. \(\sqrt{gR \left(\dfrac{\mu_{s} + \tanθ}{1 - \mu_{s} \tanθ}\right)} \)
2. \(\sqrt{\dfrac{g}{R} \left(\dfrac{\mu_{s} + \tanθ}{1 - \mu_{s} \tanθ}\right)}\)
3. \(\sqrt{\dfrac{g}{R^{2}} \left(\dfrac{\mu_{s} + \tanθ}{1 - \mu_{s} \tanθ}\right)} \)
4. \(\sqrt{gR^2 \left(\dfrac{\mu_{s} + \tanθ}{1 - \mu_{s} \tanθ}\right)}\)
1. \( 16~ \text{ms}^{-1} \)
2. \( 4 ~\text{ms}^{-1} \)
3. \( 2 ~\text{ms}^{-1} \)
4. \( 8~ \text{ms}^{-1}\)
- 1(current)
Q. No.
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