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?

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

$A$ block of mass $m$ is kept on a horizontal turntable at a distance $x$ from the center. If the coefficient of friction between the block and the surface of the turntable is $\mu$,what is the maximum angular speed of the table so that the block does not slip?

$A$ body of mass $200 \text{ g}$ is tied to a spring of spring constant $12.5 \text{ N/m}$,while the other end of the spring is fixed at point '$O$'. If the body moves about '$O$' in a circular path on a smooth horizontal surface with a constant angular speed of $5 \text{ rad/s}$,then the ratio of the extension in the spring to its natural length will be:

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 $g = 10 \, m \, s^{-2}$)

$A$ car sometimes overturns while taking a turn. When it overturns,which wheel leaves the ground first?