$A$ car is moving on a horizontal circular road of radius $0.1 \, km$ with constant speed. If the coefficient of friction between the tyres of the car and the road is $0.4$,then the speed of the car may be ......... $m/s$ $(g = 10 \, m/s^2)$.

$A$ 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

$A$ coin placed on a rotating table just slips if it is placed at a distance $4r$ from the centre. On doubling the angular velocity of the table,the coin will just slip when at a distance from the centre equal to

$A$ $70 \; kg$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3 \; m$ rotating about its vertical axis. The coefficient of friction between the wall and his clothing is $0.15$. What is the minimum rotational speed (in $rad/s$) of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed? (Take $g = 10 \; m/s^2$)

$A$ small object placed on a rotating horizontal turntable just slips when it is placed at a distance $4\, cm$ from the axis of rotation. If the angular velocity of the turntable is doubled,the object slips when its distance from the axis of rotation is (in $, cm$)

$A$ vehicle is moving with speed $v$ on a curved road of radius $r$. The coefficient of friction between the vehicle and the road is $\mu$. The angle $\theta$ of banking needed is given by