$A$ circular path of radius $75 \ m$ is banked at an angle of $\tan^{-1}(0.2)$. If the coefficient of static friction between the tyres of the car and the circular path is $0.1$, then the maximum permissible speed of the car to avoid slipping is (in $m/s$)

The maximum speed of a car on a road turn of radius $30\,m$; if the coefficient of friction between the tyres and the road is $0.4$; will be ........ $m/s$. (in $.84$)

$A$ large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in the figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is:

$A$ car of mass $m$ is moving on a level circular track of radius $R.$ If $\mu_s$ represents the static friction between the road and tyres of the car,the maximum speed of the car in circular motion is given by

$A$ 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 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 $m/s.$