$A$ road is $10\, m$ wide. Its radius of curvature is $50\, m$. The outer edge is raised above the inner edge by a distance of $1.5\, m$. This road is most suited for the velocity of ........ $m/s$. (in $.5$)

$A$ horizontal curve on a racing track is banked at a $45^o$ angle. When a vehicle goes around this curve at the curve's safe speed (no friction needed to stay on the track),what is its centripetal acceleration?

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

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

$A$ train has to negotiate a curve of radius $r \ m$. The distance between the rails is $\ell \ m$ and the outer rail is raised above the inner rail by a distance of $h \ m$. If the angle of banking is small,the safety speed limit on this banked track is:

$A$ road is banked at an angle of $30^o$ to the horizontal for negotiating a curve of radius $10\sqrt{3} \ m$. At what velocity will a car experience no friction while negotiating the curve? ............... $km/hr$