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 $0.2$.

If a cyclist moving with a speed of $4.9 \, m/s$ on a level road can take a sharp circular turn of radius $4 \, m$,then the coefficient of friction between the cycle tyres and the road is:

$A$ motorcyclist of mass $m$ is to negotiate a curve of radius $r$ with a speed $v$. The minimum value of the coefficient of friction so that the negotiation may take place safely is

$A$ 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 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 ........ $m$.

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 ........ $m/s.$