$A$ disc of radius $5\, m$ is rotating with an angular frequency of $10\, rad/s$. $A$ block of mass $2\, kg$ is to be placed on the disc. If the coefficient of friction between the disc and the block is $\mu_s = 0.4$,find the maximum distance from the axis where the block can be placed without sliding (in $cm$).

$A$ 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:

$A$ car of mass $1500 \ kg$ is moving with a speed of $12.5 \ m/s$ on a circular path of radius $20 \ m$ on a level road. What should be the coefficient of friction between the car and the road,so that the car does not slip?

$A$ small mass $m$ rests at the edge of a horizontal disc of radius $R$. The coefficient of static friction between the mass and the disc is $\mu$. The disc is rotated about its axis at an angular velocity such that the mass slides off the disc and lands on the floor $h$ meters below. What was its horizontal distance of travel from the point it left the disc?

For a body moving in a circular path,what is the condition for no skidding if $\mu$ is the coefficient of friction?

On which road do we get maximum speed: a circular road with a slope (banked road) or a level circular road?