The block has mass $M$ and rests on a surface for which the coefficients of static and kinetic friction are ${\mu }_s$ and ${\mu }_k$ respectively. A force $F=k{t}^2$ is applied to the cable. Velocity of block at $t=2 \sec$ is $v \mathrm{m} {\mathrm{s}}^{-1}$. Then value of $\frac{23}{v}$ is  Given: $M=24 \mathrm{kg}, k=60 \mathrm{N} {\mathrm{s}}^{-2}, {\mu }_s=0.5, {\mu }_k=0.4$

 

A plank with a uniform sphere placed on it, rests on a smooth horizontal plane. Plank is pulled to right by a constant force $F$. If the sphere does not slip over the plank then 

The coefficient of static and kinetic friction between the two blocks and also between the lower block and the ground are ${\mu }_s=0.6$ and ${\mu }_k=0.4$. Find the value of tension $T$ applied on the lower block at which the upper block begins to slip relative to lower block.

The member $OA$ rotates in vertical plane about a horizontal axis through $O$ with a constant counter clockwise velocity $\omega =3 \mathrm{rad} {\mathrm{s}}^{-1}$. As it passes the position $\theta =0$, a small mass $m$ is placed upon it at a radial distance $r=0.5\mathrm{m}$. If the mass is observed to slip at $\theta =37°$, find the coefficient of friction between the mass & the member.