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

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 $m$)

$A$ truck of mass $2000 \,kg$ is moving along a circular path having a radius of curvature $10 \,m$. If the banking angle is $39^{\circ}$, then the maximum permissible speed of the truck is (Acceleration due to gravity $= 10 \,ms^{-2}$, take $\tan 39^{\circ} = 0.81$). (in $\,ms^{-1}$)

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:

Define optimum speed.

$A$ 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 ....... $m\,s^{-1}$.