Banking Angle

Q.

A civil engineer wishes to redesign the curved roadway in such a way that a car will not have to rely on friction to round the curve without skidding. In other words, a car moving at the designated speed can negotiate the curve even when the road is covered with ice. Such a ramp is usually banked, which means that the roadway is tilted toward the inside of the curve. Suppose the designated speed for the ramp is to be 10.0 m/s and the radius of the curve is 20.0 m. At what angle should the curve be banked?

1. 

2. 

3. 

4. 

Q.

A cyclist goes round a circular path of circumference 34.3 m in $\sqrt{22}$ sec. the angle made by him, with the vertical, will be

1. ${42}^{\circ }$

2. ${40}^{\circ }$

3. ${48}^{\circ }$

4. ${45}^{\circ }$

Q.

The maximum speed of a car on a road–turn of radius 30 m, if the coefficient of friction between the tyres and the road is 0.4, will be

1. 6.84 m/sec

2. 10.84 m/sec

3. 9.84 m/sec

4. 8.84 m/sec

Q.

A circular track of radius 600 m is to be designed for cars at an average speed of 180 km/hr. What should be the angle of banking of the track?

1. 

2. 

3. 

4. 

Q.

An aircraft executes a horizontal loop with a speed of 150 m/s with its, wings banked at an angle of ${120}^{\circ }$. The radius of the loop is $(g=10m/s^2)$

1. 10.6 km

2. 9.6 km

3. 7.4 km

4. 5.8 km

Q.

A cyclist taking turn bends inwards while a car passenger taking same turn is thrown outwards. The reason is

1. Cyclist has to counteract the centrifugal force while in the case of car only the passenger is thrown by this force

2. Car is heavier than cycle

3. Difference in the speed of the two

4. Car has four wheels while cycle has only two

Q.

A cyclist riding the bicycle at a speed of $14\sqrt{3}m{s}^{-1}$ takes a turn around a circular road of radius $20\sqrt{3}$ m without skidding. Given $g=9.8m{s}^{-2}$, what is his inclination to the vertical

1. ${30}^{\circ }$

2. ${90}^{\circ }$

3. ${60}^{\circ }$

4. ${45}^{\circ }$

Q. The maximum speed of a cyclist on a race track is $20\text{m/s}$ and he can bend to a maximum angle of ${45}^{\circ }$. The race track has a curve of radius $20\text{m}$. Is this race track safe for the racer? If not, what should be the angle of banking of the curve?

1. The track is not safe, ${15}^{\circ }$
2. The track is safe.
3. The track is not safe, ${10}^{\circ }$
4. The track is not safe, ${19}^{\circ }$

Q. A curved road of $50\text{m}$ radius is banked at correct angle for a given maximum speed $vm/s$. If the radius of curvature of the road is changed to $200\text{m}$ keeping the same banking angle, the maximum safe speed on the road is

1. $3v\text{m/s}$
2. $4v\text{m/s}$
3. $0.5v\text{m/s}$
4. $2v\text{m/s}$

Q. The angle which the bicycle and its rider must make with the vertical when going round a curve of $8.1\text{m}$ radius at $9m{s}^{-1}$ is (Take $g=10m/s^2$)

1. ${20}^{\circ }$
2. ${45}^{\circ }$
3. ${30}^{\circ }$
4. ${60}^{\circ }$