Assuming the coefficient of friction between the road and tyres of a car to be $0.5$,the maximum speed with which the car can move round a curve of $40.0\, m$ radius without slipping,if the road is unbanked,should be ......... $m/s$.

For a vehicle moving on a banked curved road,using a free body diagram $(FBD)$,obtain the formula for the maximum safe speed $(v_{max})$.

$A$ cyclist on a level road takes a sharp circular turn of radius $3 \; m$ $(g = 10 \; m \cdot s^{-2})$. If the coefficient of static friction between the cycle tyres and the road is $0.2$,at which of the following speeds will the cyclist not skid while taking the turn?

$A$ block of mass $10\; kg$ is in contact with the inner wall of a hollow cylindrical drum of radius $1\; m$. The coefficient of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis will be: ......$rad/s$ $(g = 10\; m/s^2)$

$A$ 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

$A$ cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed,the tendency to overturn is