The maximum safe speed of a car on a flat circular road of radius $4 \; m$ is $4.9 \; m/s$. What is the coefficient of friction between the road and the tires?

$A$ cyclist speeding at $18 \; km/h$ on a level road takes a sharp circular turn of radius $3 \; m$ without reducing the speed. The coefficient of static friction between the tyres and the road is $0.1$. Will the cyclist slip while taking the turn?

$A$ $0.5 \ kg$ 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 $g = 10 \ m/s^2$)

$A$ circular road of radius $1000\, m$ has a banking angle of $45^o$. The maximum safe speed of a car having a mass of $2000\, kg$ will be,if the coefficient of friction between the tyre and the road is $0.5$.

$A$ car moves on a horizontal circular road of radius $16 \ m$ with an increasing speed at a constant rate of $3 \ m \ s^{-2}$. If the coefficient of friction between the road and the tyres is $0.5$, then the speed at which the car will skid is (assume $g = 10 \ m \ s^{-2}$): (in $m \ s^{-1}$)

For a banked curved road,if the velocity of the vehicle $v < v_0$ (where $v_0$ is the optimum speed),what is the direction of the frictional force?