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

$A$ disc revolves with a speed of $33 \frac{1}{3} \; rev/min$,and has a radius of $15 \; cm$. Two coins are placed at $4 \; cm$ and $14 \; cm$ away from the centre of the record. If the coefficient of friction between the coins and the record is $0.15$,which of the coins will revolve with the record?

$A$ 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?

Two cars are moving on a banked circular path of radius $8 \ m$ having an angle of banking $45^{\circ}$. If the coefficients of static friction between the road and the tyres of the two cars are $0.5$ and $0.4$ respectively,then the ratio of maximum permissible speeds of the cars to avoid slipping is

$A$ cyclist leans at an angle of $30^{\circ}$ with the vertical while negotiating a circular road of radius $20 \sqrt{3} \,m$. The speed of the cycle should be

$A$ motorcyclist rides in a horizontal circle about a central vertical axis inside a cylindrical chamber of radius $r$. If the coefficient of friction between the tyres and the inner surface of the chamber is $\mu$,what is the minimum speed of the motorcyclist to prevent him from skidding? ($g$ = acceleration due to gravity)