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

The safe speed of a vehicle over a smooth banked road of radius $150\ m$ is $10\ m/s$. If the width of the road is $7.5\ m$,the height of the outer edge is: (in $m$)

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

$A$ 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 $1.5 \ m$)

$A$ car is moving with speed $v$ on a banked road of radius $50 \ m$,width $10 \ m$,and height $1.5 \ m$. The velocity $v$ of the car is ......... $m/s$.

$A$ railway track is banked for a speed $v$ by elevating the outer rail by a height $h$ above the inner rail. If the distance between the two rails is $d$,then the radius of curvature of the track is ($g$ = gravitational acceleration).