# Friction and Horizontal Circular Motion Problems

## Trending Questions

**Q.**A car is travelling on a track which has radius of curvature 50 m. What is the maximum safe speed with which the car can travel on this track? Take g=10 m/s2. Assume coefficient of friction to be 0.8.

- 10√3 m/s
- 20 m/s
- 10√5 m/s
- 10 m/s

**Q.**

A car moving at a speed of 36 km/hr is taking a turn on a circular road of radius 50 m. A small wooden plate is kept on the seat with its plane perpendicular to the radius of the circular road (figure 7-E4). A small block of mass 100 g is kept on the seat which rests against the plate. The friction coefficient between the block and the plate is μ=0.58. (a) Find the normal contact force exerted by the plate on the block. (b) The plate is slowly turned so that the angle between the normal to the plate and the radius of the road slowly increases. Find the angle at which the block will just start sliding on the plate.

**Q.**

A car moving on a horizontal road may be thrown out of the road in taking a turn

By the gravitational force

Due to lack of sufficient centripetal force

Due to rolling frictional force between tyre and road

Due to the reaction of the ground

**Q.**A stone of mass m tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

- the same throughout the motion.
- minimum at the highest position of the circular path.
- minimum at the lowest position of the circular path.
- minimum when the rope is in the horizontal position.

**Q.**A 1200 kg automobile rounds a level curve of radius 200 m, on an unbanked road with a velocity of 72 km/h. What is the minimum coefficient of static friction between the tyres and road in order that the automobile may not skid? (g=10 m/s2)

- 0.3
- 0.15
- 0.4
- 0.2

**Q.**A turn of radius 20 m is banked for the vehicle of mass 200 kg going at a speed of 10 m/s. The minimum coefficient of static friction required, if the vehicle moves with a speed of 15m/s is given by N8. Then, N is

[Take g=10 m/s2]

**Q.**A car travels at a constant speed of 30 m/s around a level circular bend of radius 100 m. What is the minimum coefficient of static friction between the tires and the road in order for the car to go round the bend without skidding?

- 0.8
- 0.55
- 0.7
- 0.9

**Q.**A car travelling on a level road with a curve of radius 32 m. The coefficient of static friction between the road and tyre of car is 0.2. What speed will put the car on verge of sliding? (g=10 m/s2)

- 10 m/s
- 8 m/s
- 13 m/s
- 6 m/s

**Q.**A circular racing track of radius 300 m is banked at an angle of 17∘ with the horizontal. If the coefficient of static friction (μs) between the wheels of the racing car and the road is 0.2, what is the maximum permissible speed to avoid slipping? Take g=10 m/s2. Use the given data: tan17∘=0.30, sin17∘=0.29, cos17∘=0.96 and 0.500.94≃0.5

- 10√15 m/s
- 3√35 m/s
- 50 m/s
- 5√15 m/s

**Q.**A train of mass m moves with a velocity v on the equator from east to west. If ω is the angular speed of earth about its axis and R is the radius of the earth then the normal reaction acting on the train is

- mg[1−(ωR−2v)ωg−v2Rg]
- mg[1−2(ωR−v)ωg−v2Rg]
- mg[1−(ωR−2v)ωg+v2Rg]
- mg[1−2(ωR−v)ωg+v2Rg]

**Q.**A circular curve of highway is designed for traffic moving at 72 km/h. If the radius of the curved path is 100 m, then 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 car of mass 800 kg moves on a horizontal circular track of radius 40 m. If the coefficient of static friction (μs) is 0.5, then the maximum velocity with which the car can move will be

- 20 m/s
- 25 m/s
- 15 m/s
- 14 m/s

**Q.**A car of 800 kg negotiates a banked curve of radius 160 m on a smooth road. If the banking angle is 60∘, find the normal force between the tyres and the road. (g=10 m/s2)

- 16000 N
- 8000√3 N
- 4000 N
- 4000√3 N

**Q.**A train of mass 104 kg rounds a curve of radius 100 m at a speed of 10 m/s. At what angle the track be banked in order to have no thrust on the rails? (g=10 m/s2)

- tan−1(110)
- tan−1(10)
- tan−1(120)
- tan−1(1100)

**Q.**Assertion :If the earth suddenly stops rotating about its axis, the n acceleration due to gravity will become the same at all places. Reason: The value of acceleration due to gravity is independent of rotation of the earth.

- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- Assertion is correct but Reason is incorrect
- Assertion is incorrect but Reason is correct

**Q.**A small mass m starts sliding down a smooth and stationary semi-circular track. Which of the following graph best represents the variation of the magnitude of the force applied by the track on the mass and the angle θ ? ( assume initially θ=0)

**Q.**A stunt driver of mass 60 kg rides a bike inside a hollow metallic sphere of radius 45 m. Assume the bike moves in the central plane of the sphere. If the coefficient of static friction between the wheels of the bike and the metal surface is 0.8, what must be the minimum speed of the driver so that he does not crash? Take g=10 m/s2.

- 40 m/s
- 23.72 m/s
- 25.72 m/s
- 50 m/s

**Q.**A train of mass 104 kg rounds a curve of radius 100 m at a speed of 10 m/s. At what angle the track be banked in order to have no thrust on the rails? (g=10 m/s2)

- tan−1(110)
- tan−1(10)
- tan−1(120)
- tan−1(1100)

**Q.**A chain in the shape of circular loop of mass m and radius R is placed on a frictionless surface. Loop is given an angular velocity of ω as shown in the figure. Tension in the chain is

- mω2R
- mω2R2π
- mω2R2
- mω2Rπ

**Q.**An unbanked curve has a radius of 60m. Coefficient of friction between the tyre of truck and road is 0.75. The distance between two front wheel of truck is 2m. If the truck exceeds the speed of safe limit, then select the correct statement and justify your asnwer.

1) Inner wheels leave the ground first.

2) Outer wheels leave the ground first.

**Q.**A car is negotiating a curved road of radius R. The road is banked at an angle θ. the coefficient of friction between the tyres of the car and the road is μs. The maximum safe velocity on this road is

- √gR2μs+tanθ1−μstanθ
- √gRμs+tanθ1−μstanθ
- √gRμs+tanθ1−μstanθ
- √gR2μs+tanθ1−μstanθ

**Q.**A turn of radius 20 m is banked for the vehicle of mass 200 kg going at a speed of 10 m/s. The minimum coefficient of static friction required, if the vehicle moves with a speed of 15m/s is given by n8. Then, n is

[Take g=10 m/s2]

**Q.**A car travelling on a level road with a curve of radius 32 m. The coefficient of static friction between the road and tyre of car is 0.2. What speed will put the car on verge of sliding? (g=10 m/s2)

- 10 m/s
- 8 m/s
- 13 m/s
- 6 m/s

**Q.**A car is travelling on a track which has radius of curvature 50 m. What is the maximum safe speed with which the car can travel on this track? Take g=10 m/s2. Assume coefficient of friction to be 0.8.

- 10√3 m/s
- 10 m/s
- 20 m/s
- 10√5 m/s

**Q.**If a block moving up an inclined plane at 30o with a velocity of 5m/s, stops after 0.5s, then coefficient of friction will be nearly

- 0.5
- 0.6
- 0.9
- 1.1

**Q.**The rotation of the earth about its axis speed up such that a man on the equator becomes weightless. In such a situation, what would be the duration of one day?

- 2π√R/g
- 12π√R/g
- π√R/g
- 12π√Rg

**Q.**Motorcycle rider is moving in a hollow sphere in a horizontal circle of radius 5 m with constant speed 12 m/s. Acceleration due to gravity is 9.8 m/s2. The coefficient friction between tires of the motorcycle and the inner surface of the sphere is:

- 2.94
- 0.58
- 0.34
- 0.23

**Q.**A car travelling on a level road with a curve of radius 32 m. The coefficient of static friction between the road and tyre of car is 0.2. What speed will put the car on verge of sliding? (g=10 m/s2)

- 10 m/s
- 8 m/s
- 13 m/s
- 6 m/s

**Q.**A particle is moving around a circular path with uniform angular speed (ω). The radius of the circular path is (r). The acceleration of the particle is?

- ω2r
- ωr
- vω
- vr

**Q.**The work done against force of friction is: (consider ideal quantites )

- 8.7 J
- 10.7 J
- 7.8 J
- 12.7 J