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

$A$ circular path of radius $75 \ m$ is banked at an angle of $\tan^{-1}(0.2)$. If the coefficient of static friction between the tyres of the car and the circular path is $0.1$, then the maximum permissible speed of the car to avoid slipping is (in $m/s$)

$A$ stone of mass $0.25 \; kg$ tied to the end of a string is whirled round in a circle of radius $1.5 \; m$ with a speed of $40 \; rev./min$ in a horizontal plane. What is the tension in the string? What is the maximum speed in $m/s$ with which the stone can be whirled around if the string can withstand a maximum tension of $200 \; N$ (in $; m/s$)?

$A$ motorcyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius '$R$' metre. If the coefficient of friction between the wall and the tyres is '$\mu_{s}$',then the minimum speed required is ($g=$ acceleration due to gravity).

How is centripetal force provided during motion on a level circular path?

Is the maximum safe speed of a vehicle on a banked curved road higher or lower than on a flat curved road?