A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30°$, the box starts to slip and slides $4.0 \mathrm{m}$ down the plank in $4.0 \mathrm{s}$. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

 

Two stones of masses $m$ and $2m$ are whirled in horizontal circles, the heavier one in radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of lighter stone is $n$ times that of the tangential speed of the heavier stone. They are reported to experience the same centripetal force. The value of $n$ is, 

The force $‘F\text{'}$ acting on a particle of mass $‘m\text{'}$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8 \mathrm{s}$ is: