Roads are banked on curves so that

$A$ road is $10 \text{ m}$ wide. Its radius of curvature is $50 \text{ m}$. The outer edge is above the inner edge by a distance of $1.5 \text{ m}$. This road is most suited for the velocity $[g = 9.8 \text{ m/s}^2]$: (in $\text{ m/s}$)

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

On a railway curve,the outside rail is laid higher than the inside one so that the resultant force exerted on the wheels of the rail car by the tops of the rails will:

$A$ 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 ......... $m/s$.

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