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Q. No.A car with a mass of \(200\) kg is moving along a circular track with a radius of \(70\) m at an angular velocity of \(0.2\) rad/s. What is the magnitude of the centripetal force acting on the car?
1. \(560\) N
2. \(400\) N
3. \(360\) N
4. \(200\) N
1. \(560\) N
2. \(400\) N
3. \(360\) N
4. \(200\) N
Subtopic: Banking of Roads |
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Level 1: 80%+
JEE
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Given below are two statements:
| Assertion (A): | On a rainy day, it is difficult to drive a car or a bus at a high speed. |
| Reason (R): | The value of the coefficient of friction is lowered when the surface is wetted. |
| 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: Banking of Roads |
88%
Level 1: 80%+
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A curve in a level road has a radius of \(75\) m. The maximum speed of a car turning this curved road can be \(30\) m/s without skidding. If the radius of the curved road is changed to \(48\) m and the coefficient of friction between the tyres and the road remains the same, then the maximum allowed speed would be:
1. \(12\) m/s
2. \(24\) m/s
3. \(32\) m/s
4. \(44\) m/s
1. \(12\) m/s
2. \(24\) m/s
3. \(32\) m/s
4. \(44\) m/s
Subtopic: Banking of Roads |
87%
Level 1: 80%+
JEE
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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. | \(v=\sqrt{Rg \mathrm{~cot \theta}}\) |
Subtopic: Banking of Roads |
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Level 1: 80%+
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A car is negotiating a curved road of radius R. The road is banked at angle . The coefficient of friction between the tyres of the car and the road is . The maximum safe velocity on this road is
1.
2.
3.
4.
Subtopic: Banking of Roads |
86%
Level 1: 80%+
NEET - 2016
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A cyclist speeding with uniform velocity on a level road takes a sharp circular turn of radius \(4~\text{m}\) without reducing the speed. The coefficient of static friction between the tyres and the road is \(0.4\). What is the maximum speed at which the cyclist can move without slipping? \(\left (\text{take} ~g=10~ \text{ms}^{-2} \right )\)
1. \( 16~ \text{ms}^{-1} \)
2. \( 4 ~\text{ms}^{-1} \)
3. \( 2 ~\text{ms}^{-1} \)
4. \( 8~ \text{ms}^{-1}\)
1. \( 16~ \text{ms}^{-1} \)
2. \( 4 ~\text{ms}^{-1} \)
3. \( 2 ~\text{ms}^{-1} \)
4. \( 8~ \text{ms}^{-1}\)
Subtopic: Banking of Roads |
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Level 1: 80%+
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A cyclist speeding at \(5\) ms-1 on a level road takes a sharp circular turn of radius \(5\) m without tilting and reducing the speed. What should be the minimum value of the coefficient of static friction between the tyres and the road so that the cyclist will not slip while taking the turn? (take \(g=10\) ms-2)
1. \(0.50\)
2. \(0.25\)
3. \(0.20\)
4. \(0.15\)
1. \(0.50\)
2. \(0.25\)
3. \(0.20\)
4. \(0.15\)
Subtopic: Banking of Roads |
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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. \(37^\circ\)
1. \(30^\circ\)
2. \(45^\circ\)
3. \(53^\circ\)
4. \(37^\circ\)
Subtopic: Banking of Roads |
77%
Level 2: 60%+
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Links
A train moves along a circular track of radius \(R\) with speed \(v.\) The track has a width \(w\) \( (w\ll R) .\) To ensure safe motion without relying on friction, the outer rail is elevated above the inner rail. What should be the required elevation of the outer track?
| 1. | \(\dfrac{v^2 w}{R g}\) | 2. | \(\dfrac{v^2 w}{2R g}\) |
| 3. | \(\dfrac{gw v^2}{R}\) | 4. | \(\dfrac{R}{g w v^2}\) |
Subtopic: Banking of Roads |
76%
Level 2: 60%+
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