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. |
A train runs along an unbanked circular track of radius \(30\) m at a speed of \(54\) km/h. The mass of the train is \(10^{6}\) kg. What is the angle of banking required to prevent wearing out of the rail?
1. | \(30^\circ\) | 2. | \(45^\circ\) |
3. | \(53^\circ\) | 4. | \(37^\circ\) |
A circular racetrack of radius \(300~\text m\) is banked at an angle of \(15^\circ.\) If the coefficient of friction between the wheels of a race-car and the road is \(0.2,\) what is the (a) optimum speed of the race-car to avoid wear and tear on its tyres, and (b) maximum permissible speed to avoid slipping?
1. | \(v_0=28.1\) m/s and \(v_{max}=38.1\) m/s |
2. | \(v_0=38.1\) m/s and \(v_{max}=28.1\) m/s |
3. | \(v_0=0\) m/s and \(v_{max}=28.1\) m/s |
4. | \(v_0=38.1\) m/s and \(v_{max}=100\) m/s |