A coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of from the centre $............\,cm$

$Assertion$ : On a rainy day it is difficult to drive a car or bus at high speed.
$Reason$ : The value of coefficient of friction is lowered due to wetting of the surface

A wooden block of mass $M$ resting on a rough horizontal surface is pulled with a force $F$ at an angle $\phi $ with the horizontal. If $\mu $ is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is

A cylinder of mass $10\,kg$ is sliding on a plane with an initial velocity of $10\,m/s$. If coefficient of friction between surface and cylinder is $ 0.5$, then before stopping it will describe ............. $\mathrm{m}$

A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta>\mu$. The block is held stationary by applying a force $\mathrm{P}$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $\mathrm{P}$ is varied from $\mathrm{P}_1=$ $m g(\sin \theta-\mu \cos \theta)$ to $P_2=m g(\sin \theta+\mu \cos \theta)$, the frictional force $f$ versus $P$ graph will look like

Abody is placed on a rough inclined plane of inclination $\theta$ .As the angle $\theta$ is increased from $0^o$ to $90^o$ the contact force between the block and the plane