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

Roads are banked on curves so that

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

Write the formula for the maximum permissible speed of a vehicle moving on a smooth banked circular track.

$Assertion$ : There is a stage when frictional force is not needed at all to provide the necessary centripetal force on a banked road.
$Reason$ : On a banked road,due to its inclination the vehicle tends to remain inwards without any chances of skidding.

$A$ railway line is taken round a circular arc of radius $1000 \ m$,and is banked by raising the outer rail $h \ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20 \ ms^{-1}$,then the value of $4g \tan \theta$ is equal to: (The distance between the rails is $1.5 \ m$)