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Q. No.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 |
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Level 1: 80%+
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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: Banking of Roads |
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Level 2: 60%+
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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%+
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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 |
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Level 2: 60%+
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A car of \(800\) kg is taking turn on a banked road of radius \(300\) m and angle of banking \( 30°\). If coefficient of static friction is \(0.2\) then the maximum speed with which car can negotiate the turn safely : (\(g=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\))
1. \(51.4\) m/s
2. \(102.8\) m/s
3. \(70.4\) m/s
4. \(264\) m/s
Subtopic: Banking of Roads |
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Level 2: 60%+
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A cyclist travels at a speed of \(7~\text{km/hr}\) on an unbanked road and takes a sharp circular turn of radius \(2~\text{m}\) without reducing speed. The coefficient of static friction between the tyres and the road is \(0.2.\)
| Statement I: | The cyclist will be able to negotiate the turn without slipping. |
| Statement II: | If the same turn of radius \(2~\text{m}\) is taken on a road banked at \(45^\circ,\) the cyclist can travel at a speed of \(18.5~\text{km/hr}\) around the curve without slipping. |
| 1. | Statement I is incorrect and Statement II is correct |
| 2. | Both Statement I and Statement II are correct |
| 3. | Statement I is correct and Statement II is incorrect |
| 4. | Both Statement I and Statement II are incorrect |
Subtopic: Banking of Roads |
Level 3: 35%-60%
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The normal reaction \('N'\) for a vehicle of \(800~\text{kg}\) mass, negotiating a turn on a \(30^\circ\) banked road at the maximum possible speed without skidding is:
(given \(\cos30^\circ=0.87,~~\mu_s=0.2\))
1. \(6.96\times10^3~\text{kg m/s}^2\)
2. \(10.2\times10^3~\text{kg m/s}^2\)
3. \(12.4\times10^3~\text{kg m/s}^2\)
4. \(7.2\times10^3~\text{kg m/s}^2\)
(given \(\cos30^\circ=0.87,~~\mu_s=0.2\))
1. \(6.96\times10^3~\text{kg m/s}^2\)
2. \(10.2\times10^3~\text{kg m/s}^2\)
3. \(12.4\times10^3~\text{kg m/s}^2\)
4. \(7.2\times10^3~\text{kg m/s}^2\)
Subtopic: Banking of Roads |
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A particle of mass \(m\) is suspended from a ceiling through a string of length \({L}.\) The particle moves in a horizontal circle of radius \({r}\) such that \({r}=\frac{{L}}{\sqrt2}. \) The speed of the particle will be:
1. \(\sqrt{{rg}}\)
2. \(\sqrt{\frac{{rg}}{2}} \)
3. \(2\sqrt{{rg}}\)
4. \(\sqrt{{2rg}} \)
1. \(\sqrt{{rg}}\)
2. \(\sqrt{\frac{{rg}}{2}} \)
3. \(2\sqrt{{rg}}\)
4. \(\sqrt{{2rg}} \)
Subtopic: Banking of Roads |
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A body of mass \(200~\text g\) is tied to a spring constant of \(12.5 ~\text{N/m},\) while the other end of the spring is fixed at a point \(O.\) If the body moves about \(O\) in a circular path on a smooth horizontal surface with a constant angular speed of \(5 ~\text{rad/s}.\) Then the ratio of extension in the spring to its natural length will be:
1. \(2 : 5\)
2. \(1 : 1\)
3. \(1 : 2\)
4. \(2 : 3\)
1. \(2 : 5\)
2. \(1 : 1\)
3. \(1 : 2\)
4. \(2 : 3\)
Subtopic: Banking of Roads |
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A car of mass \(m\) is moving on a banked curve of radius \(r\) and banking angle \(\theta.\) To prevent the car from slipping, the maximum permissible speed is \(v_0.\) The coefficient of friction \(\mu\) between the tyres of the car and the road is given by:
| 1. | \(\mu=\dfrac{v_0^2-r g \tan \theta}{r g-v_0^2 \tan \theta} \) | 2. | \(\mu=\dfrac{v_0^2-r g \tan \theta}{r g+v_0^2 \tan \theta} \) |
| 3. | \(\mu=\dfrac{v_0^2+r g \tan \theta}{r g+v_0^2 \tan \theta} \) | 4. | \(\mu=\dfrac{v_0^2+r g \tan \theta}{r g-v_0^2 \tan \theta}\) |
Subtopic: Banking of Roads |
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