The radius of a horizontal curved road is $20 \ m$ and the coefficient of friction between the road and the vehicle's tires is $0.25$. What is the safe speed of the vehicle on this road (in $m/s$)? $(g = 9.8 \ m/s^2)$

The radius of a curved road is $R$,and the width of the road is $b$. The outer edge of the road is raised by $h$ with respect to the inner edge so that a car with velocity $V$ can pass safely over it. The value of $h$ is ($g =$ acceleration due to gravity).

$A$ vehicle is moving with speed $v$ on a curved road of radius $r$. The coefficient of friction between the vehicle and the road is $\mu$. The angle $\theta$ of banking needed is given by

$A$ car is moving on a circular level road of curvature $300\,m.$ If the coefficient of friction is $0.3$ and acceleration due to gravity is $10\,m/s^2,$ the maximum speed the car can have is ........ $km/hr.$

$A$ cyclist speeding at $18 \; km/h$ on a level road takes a sharp circular turn of radius $3 \; m$ without reducing the speed. The coefficient of static friction between the tyres and the road is $0.1$. Will the cyclist slip while taking the turn?

$A$ 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 $^{\circ}$)