With what minimum velocity should block be projected from left end $A$ towards end $B$ such that it reaches the other end $B$ of conveyer belt moving with constant velocity $v$. Friction coefficient between block and belt is $\mu$ .

A block of $7\,kg$ is placed on a rough horizontal surface and is pulled through a variable force $F$ (in $N$ ) $= 5\,t$ , where $'t'$ is time in second, at an angle of $37^o$ with the horizontal as shown in figure. The coefficient of static friction of the block with the surface is one. If the force starts acting at $t = 0\,s$ . Find the time at which the block starts to slide ......... $\sec$ (Take $g = 10\,m/s^2$ )

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 ...... $\%$

A bullet of mass $20\, g$ travelling horizontally with a speed of $500 \,m/s$ passes  through a wooden block of mass $10.0 \,kg$ initially at rest on a surface. The bullet  emerges with a speed of $100\, m/s$ and the block slides $20 \,cm$ on the surface  before coming to rest, the coefficient of friction between the block and the surface. $(g = 10\, m/s^2)$

In the diagram, $BAC$ is a rigid fixed rough wire and angle $BAC$ is $60^o$. $P$ and $Q$ are two identical rings of mass $m$ connected by a light elastic string of natural length $2a$ and elastic constant $\frac{mg}{a}$. If $P$ and $Q$ are in equilibrium when $PA = AQ = 3a$ then the least coefficient of friction between the ring and the wire is $\mu$. Then value of $\mu + \sqrt 3 $ is :-

A block of mass $1\,kg$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$ . If the acceleration of the truck is $5\,m\,s^{-2}$ . The frictional force acting on the block is ........ $N$