$A$ cyclist moves on a circular track of radius $100 \ m$. If the coefficient of friction is $0.2$,then the maximum velocity with which the cyclist can take the turn while leaning inwards is ...... $m/s$.

Obtain the formula for the maximum safe speed $(v_{max})$ of a vehicle on a level curved road.

$A$ hemispherical bowl of radius $r$ is rotating about its vertical axis of symmetry. $A$ small block kept in the bowl rotates with the bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is $\theta$,then find the angular speed $\omega$ at which the bowl is rotating.

$A$ $100 \, kg$ car is moving with a maximum velocity of $9 \, m/s$ across a circular track of radius $30 \, m$. The maximum force of friction between the road and the car is ........ $N$.

$A$ car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is $\mu_s$. The maximum safe velocity on this road is

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