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?

$A$ small mass $m$ rests at the edge of a horizontal disc of radius $R$. The coefficient of static friction between the mass and the disc is $\mu$. The disc is rotated about its axis at an angular velocity such that the mass slides off the disc and lands on the floor $h$ meters below. What was its horizontal distance of travel from the point it left the disc?

$A$ 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 $g = 10 \text{ ms}^{-2}$)

$A$ 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:

$A$ coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table is halved,it will just slip when placed at a distance of $............\,cm$ from the center.

$A$ car is crossing a turn at a speed of $10\,m/s$. If the coefficient of friction is $0.5$,then the minimum radius of the turn will be ........ $m$.