# Banking Angle

## Trending Questions

**Q.**A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45∘, the speed of the car is:

Take g=10 m/s2

- 20 m/s
- 30 m/s
- 15 m/s
- 25 m/s

**Q.**

A block is projected up to a rough plane of inclination $ 30°$. If the time of ascending is half the time for descending and the coefficient of friction is $ \mathrm{\mu } =\raisebox{1ex}{$ 3$}\!\left/ \!\raisebox{-1ex}{$5$}\right. \sqrt{\mathrm{n}} $. Then $ \mathrm{n}=$

2

**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

6.84 m/sec

10.84 m/sec

9.84 m/sec

8.84 m/sec

**Q.**A circular curve of a highway is designed for traffic moving at 72 km/h. If the radius of the curved path is 100 m, the correct angle of banking of the road should be given by

(Take g=10 m/s2)

- tan−1(23)
- tan−1(35)
- tan−1(25)
- tan−1(14)

**Q.**A point moves along an arc of a circle of radius R. Its velocity depends upon the distance covered `s' as v=A√s, where a is constant. The angle θ between the vector of total acceleration and tangential acceleration is:

- tanθ=√sR
- tanθ=√s2R
- tanθ=2sR
- tanθ=s2R

**Q.**

A cyclist riding the bicycle at a speed of 14√3ms−1 takes a turn around a circular road of radius 20√3 m without skidding. Given g=9.8ms−2, what is his inclination to the vertical

30∘

90∘

60∘

45∘

**Q.**

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

42∘

40∘

48∘

45∘

**Q.**A vehicle is moving without slipping or skidding on a circular road, which is rough and banked. Then choose the correct option for the possible direction of friction

- Up the incline
- Down the incline
- Both (a) and (b)
- None of the above

**Q.**A metre gauge train is moving at a speed of 36 km/hr along a curved track of radius 10√3 m. Find the height of the outer rail with respect to the inner rail, so that there is no side pressure on the rails. Take g=10 m/s2 and the width of the track to be 1 m.

- 0.8 m
- 0.5 m
- 1 m
- 0.6 m

**Q.**A car is moving on a circular track of radius R. The road is banked at an angle θ. μs is the coefficient of static friction between the car and the track. Find the maximum speed with which the car can move safely on the track.

- [rg(cosθ+μssinθ)cosθ−μssinθ]12
- [rg(sinθ+μscosθ)cosθ−μssinθ]12
- None
- [rg(sinθ+μscosθ)cosθ+μssinθ]12

**Q.**The maximum safe speed for a banked road is intended to be increased by 20%. If the angle of banking is not changed, then the radius of curvature of the road should be changed from 30 m to

**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?

30∘

tan−113

60∘

tan−112

**Q.**A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45∘, the speed of car is (Take g=10 m/s2)

- 30ms−1
- 20ms−1
- 10ms−1
- 5ms−1

**Q.**

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 106 kg. What provides the centripetal force required for this purpose - The engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

**Q.**The angle which the bicycle and its rider must make with the vertical when going round a curve of 8.1 m radius at 9 ms−1 is (Take g=10 m/s2)

- 20∘
- 45∘
- 30∘
- 60∘

**Q.**A railway track is banked by making the outer rail 10 cm higher than the inner rail. The distance between the rails is 2 m. If the speed limit for trains on this track is 72 km/h, what will be the radius of curvature of the turn for safe travelling? Take g=10 m/s2.

- 80 m
- 500 m
- 800 m

- 1000 m

**Q.**

A track consists of two circular parts ABC and CDE of equal radius 100 m and joined smoothly as shown in figure (7-E1). Each part subtends a right angle at its centre.A cycle weighing 100 kg together with the rider travels at a constant speed of 18 km/h on the track. (a) Find the normal contact force by the road on the cycle when it is at B and at D. (b) Find the force of friction exerted by the track on the tyres when the cycle is at B, C and D. (c) Find the normal force between the road and the cycle just before and just after the cycle crosses C. (d) What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed ? Take g=10 m/s2.

**Q.**

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

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

Car is heavier than cycle

Difference in the speed of the two

Car has four wheels while cycle has only two

**Q.**

What is the normal force in vertical circular motion?

**Q.**Statement I : On a banked curved road, vertical component of normal reaction provides the necessary centripetal force.

Statement II : Centripetal force is always required for turning on a curved path.

- Both the statements I and II are incorrect.
- Statement I is incorrect and Statement II is correct.
- Both the statements I and II are correct
- Statement I is correct and Statement II is incorrect.

**Q.**A curve in a road forms an arc of radius 800 m If the road is 39.2 m wide, calculate the safe speed for turning, if the outer edge of the road is 0.5 m higher than the inner edge. Take g=9.8 m/s2.

- 15 m/s
- 20 m/s
- 5 m/s
- 10 m/s

**Q.**What is the angle of banking necessary for a curved frictionless road of radius 30 m for safe driving at a speed of 20 m/s? (Consider value of g=10 m/s2)

- tan−1(43)
- tan−1(34)
- 60∘
- tan−1(1)

**Q.**A car has to negotiate a curve of radius 200 m. By how much should the outer side of the road be raised with respect to the inner side for a speed of 72 km/h. The width of the road is 1 m. (g=10 m/s2)

- 0.2 cm
- 2 cm
- 20 cm
- None of these

**Q.**A race track banked at an angle of 37∘ has a coefficient of static friction 0.4. What is the range of the safe velocities for the cars travelling on the track, for a turn of radius 40 m? Take g=10 m/s2.

- 9 m/s to 12 m/s
- 10 m/s to 20 m/s
- √188.46 m/s to √243.32 m/s
- √107.69 m/s to √657.14 m/s

**Q.**Assertion : Improper banking of roads causes wear and tear of tyres.

Reason : The necessary centripetal force is provided by the force of friction between the tyres and the road.

Select the correct option.

- Assertion is true but the reason is false.
- Assertion and reason both are false.
- Both assertion and reason are true but the reason is not the correct explanation for the assertion.
- Both assertion and reason are true and the reason is the correct explanation for the assertion.

**Q.**A curve on a highway has a radius of curvature 40 m. The curved road is banked at an angle of 45∘ with the horizontal. If the coefficient of static friction that the road provides is μs=0.20, what is the maximum permissible speed (in m/s) limit for vehicles travelling on the road?

Obtain the answer as nearest integer value

Useful data : g=10 m/s2 , √6=2.40

**Q.**A car is moving with a speed of 60 m/s on a curved road banked at an angle of 45∘. If the coefficient of static friction between the wheels of the vehicle and the road is 0.4, what should be the minimum radius of turn for the car so that it does not skid? Take g=10 m/s2.

- 175.5 m
- 200 m
- 170 m
- 154.3 m

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

- The track is not safe, 15∘
- The track is safe.
- The track is not safe, 10∘
- The track is not safe, 19∘

**Q.**If a body is at rest on a horizontal surface which is rough, then

- frictional force between body & surface must be zero.
- frictional force between body & surface must be non-zero.
- frictional force must be less than or equal to μsN (μs =coefficient of static friction, N= normal force).
- Total contact force must be perpendicular to surface.

**Q.**A road is banked at an angle of θ=30∘ and provides a coefficient of static friction μs=0.4. The road gets seriously damaged if it experiences a normal reaction force of more than 10000 N. What should be the maximum mass of the vehicle allowed on this road?

- 666 kg
- 1000 kg
- 5000 kg
- 555 kg