$A$ motorcyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius '$R$' metre. If the coefficient of friction between the wall and the tyres is '$\mu_{s}$',then the minimum speed required is ($g=$ acceleration due to gravity).

The coefficient of static friction between the road and tyres of a car is $0.4$. The maximum permissible speed of the car is $10 \,ms^{-1}$ on a curved unbanked road. Then the maximum radius of curvature of the road is (acceleration due to gravity $= 10 \,ms^{-2}$)

$A$ cyclist moves on a circular track of radius $100 \ m$. If the coefficient of friction is $0.2$,then the maximum velocity with which the cyclist can take the turn while leaning inwards is ...... $m/s$.

$A$ hollow vertical cylinder of radius $R$ is rotated with angular velocity $\omega$ about an axis through its center. What is the minimum coefficient of static friction necessary to keep the mass $M$ suspended on the inside of the cylinder as it rotates?

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

$A$ $0.5 \ kg$ mass is in contact against the inner wall of a cylindrical drum of radius $4 \ m$ rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is $5 \ rad/s$. The coefficient of friction between the drum's inner wall surface and mass is . . . . . . . (Take $g = 10 \ m/s^2$)