Circular Motion and Banking of Roads

A circular road is banked at an angle $\theta$ for an optimum speed $V$.The vertical component of the normal reaction on a car driven at the speed $V$ on the road is equal to (in equal notations)

A particle describes a horizontal circle with uniform speed on the smooth surface of an inverted cone. The height of the horizontal plane above the vertex of the cone is $10 \mathrm{m}$. What is the speed of the particle if $g=10 \mathrm{m} {\mathrm{s}}^{-2}$?

In a uniform circular motion:

For a body moving with constant speed in a horizontal circle, which of the following remains constant?

Which force is applied to the well of death?

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

What is the angle of banking of a railway track of radius of curvature $250 \mathrm{m},$ if the maximum velocity of the train is $90\mathrm{kmph} ?$ (use $g=10 \mathrm{m}·{\mathrm{s}}^{-2}$ )

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 m is taking a circular turn of radius $\mathrm{r}$ on a frictional level road with a speed $\vartheta$. In order that the car does not skid 

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 particle describes a horizontal circle of radius r in a funnel type vessel of frictionless surface with half one angle $\theta$ (as shown in figure). If mass of the particle is m, then in dynamical equilibrium the speed of the particle must be –

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 $0.5$)

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 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?

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 ?
$\left(\mathrm{T}\mathrm{ake}=10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}\right)$

A car of 800 kg is taking turn on a banked road of
radius 300 m and angle of banking 30°. If
coefficient of static friction is 0.2 then the
maximum speed with which car can negotiate the
turn safely : $(\mathrm{g} = 10 \mathrm{m}/{\mathrm{s}}^2, \sqrt{3}=1.73)$

If a car is moving on banked road of radius $300 \mathrm{m}$ and angle of banking $30°$, then find the safe speed of the car. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.