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 is negotiating a cured road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is ${\mu }_s.$ The maximum safe velocity
on this road is

A vehicle is moving with a velocity $v$ on a curved road of width $b$ and radius of curvature $R$. For counteracting the centrifugal force on the vehicle, the difference in elevation required in between the outer and inner edges of the road is :

If radius of a curved circular track is increased by $4 \%$  then maximum safe speed :-

At a curved path of a road, the road bed is raised a little on the side away from the centre of the curved path; the slope of the road bed is given by:

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

A car is moving on a curved path with radius $R$. The banking angle of road is $\text{θ,}$ the coefficient of friction between tyres of car and road is ${\mu }_{\mathrm{s}}$. The maximum safe velocity of car is,

A road is banked at an angle of $30°$ to the horizontal for negotiating a curve of radius $10\sqrt{3} \mathrm{m}$. At what velocity will a car experience no friction while negotiating the curve?

A boy on a cycle pedals around a circle of $20$ metres radius at a speed of $20$ meters/sec. The combined mass of the boy and the cycle is $90 \mathrm{kg}$.
The angle that the cycle makes with the vertical so that it may not fall is $\left(g=9.8 \mathrm{m} {\sec }^{-2}\right)$

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 of mass $\mathrm{m}$ is moving on a level circular track of radius $R.$ If ${\mu }_{\mathrm{s}}$ represents the coefficient of static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:-