$A$ 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 $^{\circ}$)?

$A$ car is moving on a circular path and takes a turn. If $R_1$ and $R_2$ are the reactions on the inner and outer wheels respectively,then:

$A$ cyclist moves on a circular track of radius $100 \ m$. If the coefficient of friction is $0.2$,then the maximum velocity with which the cyclist can take the turn while leaning inwards is ...... $m/s$.

$A$ car is moving on a circular level road of curvature $300\,m.$ If the coefficient of friction is $0.3$ and acceleration due to gravity is $10\,m/s^2,$ the maximum speed the car can have is ........ $km/hr.$

$A$ long horizontal rod has a bead which can slide along its length,and is initially placed at a distance $L$ from one end $A$ of the rod. The rod is set in angular motion about $A$ with constant angular acceleration $\alpha$. If the coefficient of friction between the rod and the bead is $\mu$,and gravity is neglected,then the time after which the bead starts slipping is

$A$ hollow vertical cylinder of radius $R$ is rotated with angular velocity $\omega$ about an axis through its center. What is the minimum coefficient of static friction necessary to keep the mass $M$ suspended on the inside of the cylinder as it rotates?