What is the wear and tear on the tires of a vehicle moving at the optimum speed on a banked curved road?

The distance between the two tires of a car is $1.5 \, m$. The center of mass of the car is at a height of $2 \, m$ from the ground. To take a turn on a road with a radius of $120 \, m$,the speed of the car should be ........ $m/s$.

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

$A$ train runs along an unbanked circular track of radius $30 \; m$ at a speed of $54 \; km/h$. The mass of the train is $10^{6} \; kg$. What provides the centripetal force required for this purpose - the engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

$A$ $100 \, kg$ car is moving with a maximum velocity of $9 \, m/s$ across a circular track of radius $30 \, m$. The maximum force of friction between the road and the car is ........ $N$.

$A$ child is on a merry-go-round, standing at a distance $2 \ m$ from the centre. The coefficient of static friction between the child and the surface of the merry-go-round is $0.8$. At what maximum angular velocity can the merry-go-round be rotated before the child slips (in $rad/s$)? (Take $g = 10 \ m/s^2$)