$A$ 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 ........ $km/hr.$

$A$ car has to move on a level turn of radius $450\,m.$ If the coefficient of static friction between the tyre and the road is $\mu = 0.2,$ find the maximum speed the car can take without skidding in $m/s.$

In a motorcycle stunt called the "well of death",the track is a vertical cylindrical surface of $18\, m$ diameter. What should be the minimum speed of the motorcyclist in $m/s$ to prevent him from sliding down? The coefficient of friction is $0.8$ and take $g = 10\, m/s^2$.

$A$ body of mass $200 \text{ g}$ is tied to a spring of spring constant $12.5 \text{ N/m}$,while the other end of the spring is fixed at point '$O$'. If the body moves about '$O$' in a circular path on a smooth horizontal surface with a constant angular speed of $5 \text{ rad/s}$,then the ratio of the extension in the spring to its natural length will be:

The distance between the two tires of a car is $1.5 \, m$. The center of mass of the car is at a height of $2 \, m$ from the ground. To take a turn on a road with a radius of $120 \, m$,the speed of the car should be ........ $m/s$.

The maximum tension which an inextensible ring of mass $0.1\, kg/m$ can bear is $10\,N$. The maximum velocity in $m/s$ with which it can be rotated is ........ $m/s.$