$A$ car is crossing a turn at a speed of $10\,m/s$. If the coefficient of friction is $0.5$,then the minimum radius of the turn will be ........ $m$.

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

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 $g = 10\, m/s^2$.

The maximum velocity (in $m/s$) with which a car driver must traverse a flat curve of radius $150\, m$ and coefficient of friction $0.6$ to avoid skidding is ........ $m/s$.

$A$ car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$. The maximum speed with which the car can move without skidding out is

$A$ car is driven on a banked road of radius of curvature $20 \ m$ with maximum safe speed. In order to increase its safe speed by $20 \%$,without changing the angle of banking,the increase in the radius of curvature will be (Assume friction is same on the road). (in $m$)