Banking of Roads

Q. What is meant by banking of roads?

Q. A motor car is moving with speed 30m/s on a circular path of radius 500m. Its speed is increasing at the rate of $2m/s^2$. What will be its resultant acceleration?

1. $2.5m/s^2$
2. $2.7m/s^2$
3. $2m/s^2$
4. $4.5m/s^2$

Q.

What is the bending of cyclists?

Q. What is the need of banking the road?

Q.

The optimum speed for turning on a banked road is

1. $\sqrt{rg\tan \theta }$

2. $\sqrt{rgcot\theta }$

3. $\sqrt{rg\sin \theta }$

4. $\sqrt{rgsec\theta }$

Q. A circular race-car track of radius $300\text{m}$ is banked at an angle of ${15}^{\circ }$. If the coefficient of static friction between the wheels of the race-car and the road is $0.2$, what is the maximum permissible speed to avoid slipping? Take $\tan {15}^{\circ }=0.27,g=10{\text{m/s}}^2$.

1. $48\text{m/s}$
2. $17\text{m/s}$
3. $30\text{m/s}$
4. $38.60\text{m/s}$

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 circular road of radius 50 m has the angle of banking equal to 30^{\circ}. At what speed should a vehicle go on this road so that the friction is not used ?

Q. An aircraft executes a horizontal loop with a speed of $150\text{m/s}$ with it's wings banked at an angle of ${12}^{\circ }$. The radius of the loop is $(g=10{\text{m/s}}^2,\tan {12}^{\circ }=0.21)$

1. $10.7\text{km}$
2. $9.6\text{km}$
3. $7.4\text{km}$
4. $5.8\text{km}$

Q.

A block A can slide on a frictionless incline of angle $\theta$ and length l, kept inside an elevator going up with uniform velocity v in figure. Find the time taken by the block to slide down the length of the incline if it is released from the top of the incline.

Q.

If the horizontal force needed for the turn in the previous problem is to be supplied by the normal force by the road, what should be the proper angle of banking ?

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

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 Cyclist Turns Around A Curve At $15Km/hr$ If He Turns At Double The Speed The Tendency To Overturn Is :

Q.

A wheel rotates with a constant angular acceleration of $2rad/s^2$. The total acceleration of the wheel becomes $13.6rad/s^2$after 1s of the beginning of motion. Determine the radius of the wheel.

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.

What is centripetal force?

Q.

The variation of lengths of two metal rods $A$ and $B$ with change in temperature is shown in Fig. The coefficients of linear expansion ${\alpha }_A$ for the metal $A$ and the temperature $T$ will be (given ${\alpha }_B$ = 9$\times$${10}^{-6}$/ ${}^{\circ }C$)

1. α_A=3x10^-6/°C, 500°C

2. α_A=3x10^-6/°C, 222.22°C

3. α_A=27x10^-6/°C, 500°C

4. α_A=27x10^-6/°C, 222.22°C

Q.

A small block is placed on a horizontal platform which undergoes horizontal S.H.M about a mean position ‘O’.The block does not slip on the platform. Force of friction acting on the block is f.

1. ‘f’ is always directed towards ‘O’
2. f is directed towards ‘O’ when the block is moving away from ‘O’ and f is directed away from ‘O’ when the block is moving towards ‘O’
3. f = 0 when block and platform come to momentary rest at the extreme position of S.H.M
4. f is maximum when block and platform come to momentary rest at the extreme position of S.H.M

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 cyclist going around a circular road of radius $10m$ is observed to be bending inward 30${}^{\circ }$ with vertical. Frictional force acting on the cyclist is (Given: $g=10m/s^2$, mass of the cyclist is $90$ Kg)

1. $532N$
2. $800N$
3. $1559N$
4. $520N$

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 railway track is banked for a speed v, by making the height of the outer rail h higher than that of the inner rail. The distance between the rails is d. The radius of curvature of the track is r. Then,

1. $\frac{h}{d}=\frac{v^2}{rg}$
2. $tan\left(si{n}^{-1}\frac{h}{d}\right)=\frac{v^2}{rg}$
3. $ta{n}^{-1}\left(\frac{h}{d}\right)=\frac{v^2}{rg}$
4. $\frac{h}{r}=\frac{v^2}{dg}$

Q. An aircrafts executes a horizontal loop at a speed of $720km/h$ with its wings banked at ${15}^o$. What is the radius of the loop?

Q. What is banking of roads? Obtain an expression for the maximum safety speed of a vehicle moving along a curved horizontal road.

Q. A curved road is $7.5m$ wide and its outer edge is raised by $1.5m$ over the inner edge. The radius of curvature is $50m$. For what speed of the car is this road suited?$(g=10m/s^2)$:

1. $5m/s$
2. $10m/s$
3. $15m/s$
4. $20m/s$

Q.

A circular racetrack of radius $300m$ is banked at an angle of ${15}^o.$ If the coefficient of friction between the wheels of a race car and the road is $\mathrm{0.2.}$
(a) What is the optimum speed of the race car to avoid wear and tear on its tires?
(b) What is the maximum permissible speed to avoid slipping?

Q. A train has to negotiate a curve of $400$m. By how much should the outer sail be raised w.r.t. the inner rail for a speed of $48$ km/h? (given: Distance between rail $=1$m].

Q. Assertion :When an automobile while going too fast around a curve overturns, its inner wheels leave the ground first. Reason: For a safe turn the velocity of automobile should be less than the value of safe limit velocity.

1. If both Assertion and Reason are correct and Reason is the correct explanation of the Assertion
2. If both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion
3. If Assertion is true but Reason is false
4. If Assertion is false but Reason is true