For a body moving in a circular path, a condition for no skidding if $\mu $ is the coefficient of friction, is
$\frac{{m{v^2}}}{r} \leq \mu mg$
$\frac{{m{v^2}}}{r} \geq \mu mg$
$\frac{v}{r} = \mu g$
$\frac{{m{v^2}}}{r} = \mu mg$
One end of string of length $l$ is connected to a particle of mass $'m'$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed $'v',$ the net force on the particle (directed towards centre) will be ($T$ represents the tension in the string)
$A$ 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 :
A car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud, as it leaves the ground are thrown
The coefficient of friction between the tyres and the road is $0.25$. The maximum speed with which a car can be driven round a curve of radius $40 \,m$ without skidding is ........ $ms^{-1}$ (assume $g = 10 \,ms^{-2}$)
A circular road of radius $1000 \,m$ has banking angle ${45^o}$. The maximum safe speed of a car having mass $2000 \,kg$ will be, if the coefficient of friction between tyre and road is $0.5$ ....... $m/s$