$A$ car turns a corner on a slippery road at a constant speed of $10\,m/s$. If the coefficient of friction is $0.5$,the minimum radius of the arc in meters in which the car turns is:

$A$ circular road of radius $1000 \, m$ has a banking angle of $45^\circ$. The maximum safe speed of a car having mass $2000 \, kg$ will be,if the coefficient of friction between the tyre and road is $0.5$,equal to ....... $m/s$.

$A$ car is moving on a circular track banked at an angle of $45^{\circ}$. If the maximum permissible speed of the car to avoid slipping is twice the optimum speed of the car to avoid the wear and tear of the tyres,then the coefficient of static friction between the wheels of the car and the road is

Is the maximum safe speed of a vehicle on a banked curved road higher or lower than on a flat curved road?

$A$ cyclist is travelling with velocity $v$ on a curved road of radius $R$. The angle $\theta$ through which the cyclist leans inwards is given by

The maximum safe speed of a car on a horizontal road with a radius of $500\,m$ and a coefficient of friction of $0.5$ is ...... $m/s$.