$A$ wooden box lying at rest on an inclined surface of a wet wood is held at static equilibrium by a constant force $F$ applied perpendicular to the incline. If the mass of the box is $1 \ kg$,the angle of inclination is $30^{\circ}$ and the coefficient of static friction between the box and the inclined plane is $0.2$,the minimum magnitude of $F$ is (Use $g=10 \ m/s^2$)

$A$ heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is $0.25$,then the maximum fraction of length of the chain that can hang over one edge of the table is ...... $\%$

What percentage of the total length of a chain can hang off the edge of a table without sliding,given that the coefficient of friction between the chain and the table is $0.25$?

$A$ uniform rod of mass $20 \ kg$ and length $5 \ m$ leans against a smooth vertical wall making an angle of $60^{\circ}$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take $g=10 \ m/s^2$)

$STATEMENT-1$: $A$ block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. because
$STATEMENT-2$: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

An object takes $n$ times as much time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by: