A force $F=t$ is applied to block $A$ as shown in the figure. The force is applied at $t=0 \mathrm{s}$ when the system was at rest and the string is just straight without tension. Which of the following graphs gives the friction force between $B$ and horizontal surface as a function of time $t$?

 

Starting from rest, a flat car is given a constant acceleration $a_0=2 \mathrm{m} {\mathrm{s}}^{-2}$. A cable is connected to a crate $A$ of mass $50 \mathrm{kg}$ as shown. Neglect the friction between floor and car wheels and mass of pulley. The coefficient of friction between crate & floor of the car is $\mathrm{\mu } = 0.3$. The tension in the cable is –

A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\mathrm{\theta }$ to the vertical. The minimum value of the coefficient of friction between the block and the surface for which the block will remain in equilibrium is:

A plank is held at an angle $\mathrm{\alpha }$ to the horizontal (figure) on two fixed supports $A$ and $B$. The plank can slide against the supports (without friction) because of its weight $Mg$. With what acceleration and in which direction, a man of mass $m$ should move so that the plank does not move.