$A$ 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

$A$ man is standing on a rough $(\mu = 0.5)$ horizontal disc rotating with a constant angular velocity of $5 \ rad/s$. At what distance from the center should he stand so that he does not slip on the disc?

Find the maximum velocity for skidding for a car moved on a circular track of radius $100 \, m$. The coefficient of friction between the road and tyre is $0.2$.

$A$ particle is moving along the circle $x^2 + y^2 = a^2$ in an anticlockwise direction. The $x-y$ plane is a rough horizontal stationary surface. At the point $(a \cos \theta, a \sin \theta)$,the unit vector in the direction of friction on the particle is:

$A$ disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if

$A$ large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in the figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is: