Roads are banked on curves so that

What is optimum speed? Write its equation.

The radius of a curved road on a national highway is $R$. The width of the road is $b$. The outer edge of the road is raised by $h$ with respect to the inner edge so that a car with velocity $v$ can pass safely over it. The value of $h$ is

$A$ car of mass $1000\, kg$ negotiates a banked curve of radius $90\, m$ on a frictionless road. If the banking angle is $45^\circ$,the speed of the car is ....... $m\,s^{-1}$.

$A$ train has to negotiate a curve of radius $r \ m$. The distance between the rails is $\ell \ m$ and the outer rail is raised above the inner rail by a distance of $h \ m$. If the angle of banking is small,the safety speed limit on this banked track is:

What is the angle of banking of a railway track of radius of curvature $250 \,m$, if the maximum velocity of the train is $90 \,km/h$? $(g=10 \,ms^{-2})$