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

$A$ 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 ............ $m/s$ $[g = 10\,m/s^2]$.

What is optimum speed? Write its equation.

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

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 ........ $m$.

The radius of a curved road on a national highway is $R$. The width of the road is $b$. The outer edge of the road is raised by $h$ with respect to the inner edge so that a car with velocity $v$ can pass safely over it. The value of $h$ is