Two beads connected by massless inextensible string are placed over the fixed ring as shown in figure. Mass of each bead is $m$ , and there is no friction between $B$ and ring. Find minimum value of coefficient of friction between $A$ and ring so that system remains in equilibrium. ( $C \to $center of ring, $AC$ line is vertical)

......... $m/s^2$ is magnitude of acceleration of a block moving with speed $10\,m/s$ on a rough surface if coefficient of friction is $0.2$.

As shown in the figure a block of mass $10\,kg$ lying on a horizontal surface is pulled by a force $F$ acting at an angle $30^{\circ}$, with horizontal. For $\mu_{ s }=0.25$, the block will just start to move for the value of $F..........\,N$ : $\left[\right.$ Given $\left.g =10\,ms ^{-2}\right]$

A uniform chain of length $L$ which hanges partially from a table, is kept in equilibrium by friction. The maximum length that can withstand without slipping is $l$ , then coefficient of friction between the table and the chain is

A rope of length $L$ and mass $M$ is being pulled on a rough horizontal floor by a constant horizontal force $F$ = $Mg$ . The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between rope and floor is $1/2$ . Then, the tension at the midpoint of the rope is

A uniform chain of length $L$ changes partly from a table which is kept in equilibrium by friction. The maximum length that can withstand without slipping is $l$, then coefficient of friction between the table and the chain is