A motorcycle is travelling on a curved track of radius $500\,m$. If the coefficient of friction between road and tyres is $0.5$, the speed avoiding skidding will be ....... $m/s$

$A$ particle is moving in a circle :

A car of $800 \mathrm{~kg}$ is taking turn on a banked road of radius $300 \mathrm{~m}$ and angle of banking $30^{\circ}$. If coefficient of static friction is $0.2$ then the maximum speed with which car can negotiate the turn safely : $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)$

$A$ particle inside the rough surface of $a$ rotating cone about its axis is at rest relative to it at $a$ height of $1m$ above its vertex. Friction coefficient is $\mu = 0.5$, if half angle of cone is $45^o$, the maximum angular velocity of revolution of cone can be :

Obtain the formula for the maximum safe speed $(v_{max})$ of a vehicle on a level curved road.

$Assertion$ : There is a stage when frictional force is not needed at all to provide the necessary centripetal force on a banked road.
$Reason$ : On a banked road, due to its inclination the vehicle tends to remain inwards without any chances of skidding.