The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu$ is

For a banked curved road,if the velocity of the vehicle $v < v_0$ (where $v_0$ is the optimum speed),what is the direction of the frictional force?

$A$ particle on the inner rough surface of a cone rotating about its vertical axis is at rest relative to the cone at a height of $1 \ m$ above its vertex. If the coefficient of friction is $\mu = 0.5$ and the semi-vertical angle of the cone is $45^\circ$,what is the maximum angular velocity $\omega$ of the cone?

$A$ car is moving along a circular path having a coefficient of friction $0.5$ and a radius of curvature $16.2 \,m$. The maximum velocity of the car that can travel without skidding outwards is (Acceleration due to gravity $= 10 \,ms^{-2}$)

The maximum velocity (in $m/s$) with which a car driver must traverse a flat curve of radius $150 \, m$ and coefficient of friction $0.6$ to avoid skidding is

The maximum speed of a car on a road turn of radius $30\,m$; if the coefficient of friction between the tyres and the road is $0.4$; will be ........ $m/s$. (in $.84$)