Friction in Curved Roads

Q.

Consider a vehicle going on a horizontal road towards east. Neglect any force by the air. The frictional forces on the vehicle by the road

1. Is towards east if the vehicle is accelerating

2. Is zero if the vehicle is moving with a uniform velocity

3. Must be towards east

4. Must be towards west

Q. A car of mass $2000kg$ is moving with a constant speed of $10m{s}^{-1}$ on a circular path of radius $20\text{m}$ on a level road. What must be the frictional force between the car and the road so that the car does not slip on the road ?

1. ${10}^4\text{N}$
2. ${10}^3\text{N}$
3. ${10}^5\text{N}$
4. ${10}^2\text{N}$

Q.

A 1500-kg car moving o a flat, horizontal road negotiates a curve as show in figure. If the radius of the curve is 20.0 m and the coefficient of static friction between the tires and dry pavement is 0.50, find the maximum speed the car can have and still make the turn successfully.

1. 20 m/s

2. 30 m/s

3. 10 m/s

4. 40 m/s

Q. What should be the value of coefficient of static friction between the tyre and the road, when a car travelling at speed of $60km{h}^{-1}$ makes a level turn of radius $40\text{m}$?

1. $0.5$
2. $0.66$
3. $0.71$
4. $0.80$

Q. A car of mass $2000kg$ is moving with a constant speed of $10m{s}^{-1}$ on a circular path of radius $20\text{m}$ on a level road. What must be the frictional force between the car and the road so that the car does not slip on the road ?

1. ${10}^4\text{N}$
2. ${10}^3\text{N}$
3. ${10}^5\text{N}$
4. ${10}^2\text{N}$

Q. Statement I : A cyclist is moving on an unbanked road with a speed of $7{\text{kmh}}^{-1}$ and takes a sharp circular turn along a path of radius of $2\text{m}$ without reducing the speed. The static friction coefficient is $\mathrm{0.2.}$ The cyclist will not slip and pass the curve.
$(g=10{\text{m/s}}^2)$

Statement II : If the road is banked at an angle of ${45}^{\circ }$, cyclist can cross the curve of $2\text{m}$ radius with the speed of $15{\text{kmh}}^{-1}$ without slipping.

In the light of the above statements, choose the correct answer from the options given below.

1. Statement I is correct and statement II is incorrect
2. Statement I is incorrect and statement II is correct
3. Both statement I and statement II are false
4. Both statement I and statement II are true

Q. What should be the value of coefficient of static friction between the tyre and the road, when a car travelling at speed of $60km{h}^{-1}$ makes a level turn of radius $40\text{m}$?

1. $0.5$
2. $0.66$
3. $0.71$
4. $0.80$

Q. A car is moving on a levelled circular road of radius of curvature $300\text{m}$. If the coefficient of static friction is $0.3$ and acceleration due to gravity is $10m{s}^{-2}$, then maximum allowable speed for the car will be (in $km{h}^{-1})$

1. $30$
2. $81$
3. $108$
4. $162$