Banking of Roads

A car travels on a banked horizontal road with inclination $45°$. What is its maximum speed for not skidding up $\left(\mu =0.75,R=200\right)$.

A car is moving on a circular road of radius $150 \mathrm{m}$ with a coefficient of friction $0.6$. With what optimum velocity should the car be moved so that it crosses the turn safely.:

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

The minimum velocity (in $\mathrm{m}{\mathrm{s}}^{-1}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

If a cyclist moving with a speed of $4.9 \mathrm{m}/\mathrm{s}$ on a level road can take a sharp circular turn of radius $4\mathrm{ }\mathrm{m}$, then coefficient of friction between the cycle tyres and road is

A biker initially at rest, starts to move on a circular path of radius $R=\frac{200}{7} \mathrm{km}$  with tangential acceleration $a = 1 \mathrm{m} {\sec }^{-2}$ (constant in magnitude). If on an average bike runs $50 \mathrm{km} {\mathrm{litre}}^{-1}$ and initially the bike has $2 \mathrm{litre}$ petrol. The minimum value of the coefficient of friction, so, that bike will not slip during motion is 

A disc revolves with a speed of $120$ $\mathrm{rev}./\min .$ and has a radius of $15 \mathrm{cm}.$ Two coins $\mathrm{A}$ and $\mathrm{B}$ are placed at $4 \mathrm{cm}$ and $14 \mathrm{cm}$ away from the centre of the record. If the coefficient of friction between the coins and the record is $0.16.$ which of the coins will revolve with the record ?

A circular road of radius $1000 \mathrm{m}$ has banking angle $45°$. The maximum safe speed (in ${\mathrm{ms}}^{-1}$) of a car having a mass $2000 \mathrm{kg}$ will be (if the coefficient of the friction between tyre and road is $0.5$)

A car of mass $1000 \mathrm{kg}$ negotiates a banked curve of radius $90 \mathrm{m}$ on a frictionless road. If the banking angle is $45°$, the safe speed of the car is

Radius of the curved road on national highway is $P$. Horizontal width of the road is $Q$. The outer edge of the road is raised by $\mathrm{H}$ with respect to the inner edge so that a car with velocity $\mathrm{x}$ can pass safely over it the value of $\mathrm{H}$ is :-

A cyclist riding the bicycle at a speed of $14\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ takes a turn around a circular road of radius  $20\sqrt{3} \mathrm{m}$ without skidding. Given $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$, what is his inclination to the vertical.

A car is negotiating a curved road of radius $70 m$ road is banked at $45°.$ The coefficient of friction between road and tyre is $0.75 .$ The maximum safe speed on this road is :-

What is the minimum speed a car can travel on an inclined road in terms of radius of the curved path $R$, acceleration due to gravity $g$, coefficient of static friction ${\mu }_s$, and the inclined angle of the road?

A car is moving on a circular road with coefficient of friction $0.3$ and curvature $300 \mathrm{m}$. Find the maximum speed of the car. (Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.)

The coefficient of friction between the tyres and the road is given by $0.1$ . What is the maximum speed with which a cyclist can take a circular turn of radius 3 m without skidding ?
$\left(\mathrm{T}\mathrm{ake}=10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}\right)$

The maximum velocity in $\mathrm{m} {\mathrm{s}}^{-1}$ at which a car traversing a flat curve of radius $150 \mathrm{m}$ and coefficient of friction $0.6$ will not skid, is

A car moves with a constant tangential acceleration ${\omega }_t=0.62 \mathrm{m} {\mathrm{s}}^{-2}$ along a horizontal surface circumscribing a circle of radius $R=40 \mathrm{m}$. The coefficient of sliding friction between the wheels of the car and the surface is $k=0.20$. The distance that the car rides without sliding is $10\alpha$ meters and if at the initial moment of time its velocity is equal to zero then ​$\alpha =$?

What will be the maximum speed of a car on a road turn of radius $30 \mathrm{m}$, if the coefficient of friction between the tyres and the road is $0.4$?

$\left(\text{Take} g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

 A car of mass $1500 \mathrm{kg}$ is moving with a speed of $12.5 \mathrm{m}/\mathrm{s}$ on a circular path of a radius $20 \mathrm{m}$ on a level road. What should be the coefficient of friction between the car and the road, so that the car does not slip?