$A$ 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?

$A$ string just breaks under a load of $50 \ kg$. $A$ mass of $1 \ kg$ is attached to one end of this string $10 \ m$ long and is rotated in a horizontal circle. Calculate the greatest number of revolutions that the mass can make in one second without breaking the string. (Take $g = 10 \ m/s^2$)

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

$A$ car turns a corner on a slippery road at a constant speed of $10\,m/s$. If the coefficient of friction is $0.5$,the minimum radius of the arc in meters in which the car turns is:

For a vehicle moving on a banked curved road,using a free body diagram $(FBD)$,obtain the formula for the maximum safe speed $(v_{max})$.

The maximum safe speed of a car on a horizontal road with a radius of $500\,m$ and a coefficient of friction of $0.5$ is ...... $m/s$.