Banking of Roads

Q.

A road is banked such that a vehicle can go in the middle of it with a constant velocity of 40 m/s. What will happen if the velocity is decreased and why?
Imagine friction is not present

1. The vehicle slide up as Normal by ground will increase

2. The vehicle will slide down as Normal by ground will decrease.

3. The vehicle will slide down as centripetal force mv²/R has to be constant

4. None of these

Q.

A curve has a radius of 50 meters and a banking angle of 15º. What is the ideal, or critical, speed (the speed for which no friction is required between the car's tires and the surface) for a car on this curve?

1. 7 m/s
2. 11 m/s
3. 14 m/s
4. 16 m/s

Q. A motorcycle is going on an over-bridge of radius R at a constant speed. As the motorcycle is ascending on the over-bridge, the normal force on it.

1. increases
2. decreases
3. remains the same
4. fluctuates

Q. A turn of radius $20$ m is banked for the vehicle going at speed of $36$ km/hr. If the coefficient of static friction between the road and the tyre is $0.4$. What of the following speeds are possible such that the vehicle neither slips down nor skids up ?

1. $20$ km/hr
2. $30$ km/hr
3. $40$ km/hr
4. $50$ km/hr

Q. A car is moving at 20 m/s on a banked racing circular track of radius $\frac{160}{3}m$, and there is no wear and tear of tyres. Height difference [in meter] between two rare or front wheels if width of car is 1m is$[g=10m/s^2]$ Write until two digits after the decimal point.

Q. A circular race track of radius $85\text{m}$ is banked at angle of ${37}^{\circ }$ If the coefficient of friction between the wheels of a race-car and the road is $0.2$, then the maximum possible speed to avoid slipping is $(\tan {37}^{\circ }=\frac{3}{4})$

1. $\sqrt{950}\frac{m}{s}$
2. $\sqrt{1050}\frac{m}{s}$
3. $\sqrt{550}\frac{m}{s}$
4. $\sqrt{850}\frac{m}{s}$

Q. A curved road of radius $50m$ is banked at correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should be changed to

1. $25\text{m}$
2. $100\text{m}$
3. $150\text{m}$
4. $200\text{m}$

Q. A circular road of radius $1000\text{m}$ has a banking angle of ${45}^{\circ }$. The maximum safe speed (in $\text{m/s}$) of a car having a mass $2000\text{kg}$ will be (if the coefficient of friction between the tyres and the road is $0.3$) (Take $g=10{\text{m/s}}^2$)

1. $136$
2. $124$
3. $99$
4. $86$

Q. A turn of radius $20\text{m}$ is banked for vehicles going at a speed of $36\text{km/h}$. If the coefficient of friction between the road and the tyres is $0.4$, what are the possible speeds of a vehicle so that it neither slips down nor skids up ?

1. $v_{min}=4\text{m/s};v_{max}=10\text{m/s}$
2. $v_{min}=8\text{m/s};v_{max}=12\text{m/s}$
3. $v_{min}=6\text{m/s};v_{max}=10\text{m/s}$
4. $v_{min}=4\text{m/s};v_{max}=15\text{m/s}$

Q. A road of width $20\text{m}$ forms an arc of radius $15\text{m}$, its outer edge is $2\text{m}$ higher than its inner edge. For what speed the road is banked?

1. $\sqrt{10}\text{m/s}$
2. $\sqrt{14.7}\text{m/s}$
3. $\sqrt{9.8}\text{m/s}$
4. None of these