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

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 $m$)

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

$A$ 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?

$A$ 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 maximum speed of the car is ............ $m/s$ $[g = 10\,m/s^2]$.

$Assertion$ : There is a stage when frictional force is not needed at all to provide the necessary centripetal force on a banked road.
$Reason$ : On a banked road,due to its inclination the vehicle tends to remain inwards without any chances of skidding.