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

$A$ person is driving a vehicle at a uniform speed of $5 \text{ ms}^{-1}$ on a level curved track of radius $5 \text{ m}$. The coefficient of static friction between the tyres and the road is $0.1$. Will the person slip while taking the turn with the same speed? (Take $g = 10 \text{ ms}^{-2}$)

$A$ $70 \; kg$ 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 $g = 10 \; m/s^2$)

How is centripetal force provided during motion on a level circular path?

$A$ plank is resting on a horizontal ground in the northern hemisphere of the earth at a $45^{\circ}$ latitude. Let the angular speed of the earth be $\omega$ and its radius $r_e$. The magnitude of the frictional force on the plank will be

$A$ cyclist riding a bicycle at a speed of $14 \sqrt{3} \, m/s$ takes a turn around a circular road of radius $20 \sqrt{3} \, m$ without skidding. What is his inclination to the vertical (in $^{\circ}$)?