Write the formula for the maximum safe speed of a vehicle moving on a smooth curved road of radius $r$ and banking angle $\theta$.

$A$ 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 $1.5 \ m$)

In the case of a conical pendulum,if $T$ is the tension in the string and $\theta$ is the semi-vertical angle of the cone,then the component of tension which balances the centrifugal force in the equilibrium position is

What is the speed of a vehicle moving on a flat and smooth (frictionless) circular path of radius $r$?

Why are curved roads banked?

Which component provides the centripetal force for a vehicle moving at an optimum speed on a banked road?