The maximum velocity (in $ms^{-1}$) with which a car driver must traverse a flat curve of radius $150 \,m$ and coefficient of friction $0.6$ to avoid skidding is

A car of mass $m$ is moving on a level circular track of radius $R.$ If $\mu_s $ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by

A string breaks if its tension exceeds $10$ newtons. A stone of mass $250\, gm$ tied to this string of length $10 \,cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be ..........  $rad/s$

The normal reaction $'{N}^{\prime}$ for a vehicle of $800\, {kg}$ mass, negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is $...\,\times 10^{3}\, {kg} {m} / {s}^{2}$ [Given $\left.\cos 30^{\circ}=0.87, \mu_{{s}}=0.2\right]$

$A$ 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 :

A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v$. If the coefficient of static friction between the tyres and the track is $\mu_{s},$ then the magnitude of negative lift $F_{L}$ acting downwards on the car is

(Assume forces on the four tyres are identical and $g =$ acceleration due to gravity)