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

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

The speed of a car is increased by $10\%$. If the angle of banking remains constant,the radius of the turn must be changed from $20 \ m$ to ........ $m$.

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

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 $m$)

$A$ 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?