Find the maximum velocity for skidding for a car moved on a circular track of radius $100 \, m$. The coefficient of friction between the road and tyre is $0.2$.

$A$ body of mass $M \text{ kg}$ is at the top point of a smooth hemisphere of radius $5 \text{ m}$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \text{ m/s}$. At this instant, the angle made by the radius vector of the body with the vertical is (Acceleration due to gravity $g = 10 \text{ m/s}^2$) (in $^{\circ}$)

$A$ car of mass $800 \, kg$ moves on a circular track of radius $40 \, m$. If the coefficient of friction is $0.5$,then the maximum velocity with which the car can move is ......... $m/s$.

$A$ 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:

$A$ motorcyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical wooden well of radius $8.0 \ m$,with a minimum speed of $5 \sqrt{5} \ m \ s^{-1}$. The minimum value of the coefficient of friction between the tyres and the wall of the well must be (take $g = 10 \ m \ s^{-2}$):

$A$ particle moves on a circular overbridge with constant speed. The friction coefficient varies so that the speed remains constant. Which of the following graphs shows the magnitude of friction $f$ versus the angle $\theta$?