A body is moving along a rough horizontal surface with an initial velocity $6\,\,m/s.$ If the body comes to rest after travelling $9\, m$, then the coefficient of sliding friction will be

Two blocks $A$ and $B$ of masses $5 \,kg$ and $3 \,kg$ respectively rest on a smooth horizontal surface with $B$ over $A$. The coefficient of friction between $A$ and $B$ is $0.5$. The maximum horizontal force (in $kg$ wt.) that can be applied to $A$, so that there will be motion of $A$ and $B$ without relative slipping, is

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is $0.04$ , the acceleration of the system in $\mathrm{ms}^{-2}$ is :

(Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):

A uniform wooden stick of mass $1.6 \mathrm{~kg}$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h( < l)$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough focr. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the st $ck$. The ratio $h / l$ and the frictional force $f$ at the bottom of the stick are $\left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$

A fireman of mass $60\, kg$ slides down a pole. He is pressing the pole with a force of $600 \,N$. The coefficient of friction between the hands and the pole is $0.5$, with what acceleration will the fireman slide down ........ $m/s^2$

The limiting friction is