Assuming the coefficient of friction between the road and tyres of a car to be $0.5$,the maximum speed with which the car can move round a curve of $40.0\, m$ radius without slipping,if the road is unbanked,should be ......... $m/s$.

$A$ gramophone record is rotating with an angular velocity $\omega$. $A$ coin is placed at a distance $r$ from the center of the record. The coefficient of static friction is $\mu$. The coin will revolve with the record if .......

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 $.84$)

$A$ $70 \; kg$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3 \; m$ rotating about its vertical axis. The coefficient of friction between the wall and his clothing is $0.15$. What is the minimum rotational speed (in $rad/s$) of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed? (Take $g = 10 \; m/s^2$)

$A$ boy is sitting on the horizontal platform of a joy wheel at a distance of $5 \, m$ from the center. The wheel begins to rotate and when the angular speed exceeds $1 \, rad/s$,the boy just slips. Find the coefficient of friction between the boy and the wheel. (Take $g = 10 \, m/s^2$)

What is the maximum safe speed of a car on a flat road of radius $40 \, m$ in $m \, s^{-1}$? The coefficient of friction between the road and the tires is $0.25$. (Take $g = 10 \, m \, s^{-2}$)