$A$ car is moving on a horizontal curved road with radius $50\,m$. The approximate maximum speed of the car will be $............\,ms^{-1}$,if the coefficient of friction between the tyres and the road is $0.34$. [Take $g = 10\,ms^{-2}$]

$A$ 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)

An inextensible string of length $\ell$ fixed at one end,carries a mass $m$ at the other end. If the string makes $\frac{1}{\pi}$ revolutions per second around the vertical axis through the fixed end,the tension in the string is [The string makes an angle $\theta$ with the vertical]

$A$ boy is sitting on the horizontal platform of a joy wheel at a distance of $5 \, m$ from the center. The wheel begins to rotate and when the angular speed exceeds $1 \, rad/s$,the boy just slips. Find the coefficient of friction between the boy and the wheel. (Take $g = 10 \, m/s^2$)

$A$ particle describes a horizontal circle on the smooth inner surface of a cone as shown in the figure. If the height of the circle above the vertex is $10 \ cm$,find the speed of the particle. (Given: acceleration due to gravity $g = 10 \ m/s^2$ and assume the semi-vertical angle $\theta = 45^\circ$ based on the geometry of the cone). (in $m/s$)

For a body moving in a circular path,what is the condition for no skidding if $\mu$ is the coefficient of friction?