A block of mass $m$, lying on a horizontal plane, is acted upon by a horizontal force $P$ and another force $Q$, inclined at an angle $\theta$ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is (assume $P>Q$)

A solid block of mass $2 \mathrm{kg}$ is resting inside a cube as shown in figure. The cube is moving with a velocity  $\overrightarrow{v}=5\hat{\mathrm{i}}+2\hat{\mathrm{j}} {\mathrm{ms}}^{-1}$. If the coefficient of friction between the surface of cube and block is $0.2$, then the force of friction between the block and cube is

A trolley $A$ has a simple pendulum suspended from a frame fixed to its desk. A block $B$ is in contact on its vertical side. The trolley is on horizontal rails and accelerates towards the right$\left(a\right)$ such that the block is just prevented from falling. The value of coefficient of friction between $A$ and $B$ is  $0.5$. The inclination of the pendulum to the vertical is

A block of mass $m$ is lying on a wedge having inclination angle $\alpha ={\tan }^{-1}\left(\frac{1}{5}\right)$. Wedge is moving with a constant acceleration $a=2 {\mathrm{ms}}^{-2}$. The minimum value of coefficient of friction $\mu$ so that $m$ remains stationary $\mathrm{w}.\mathrm{r}.\mathrm{t}.$wedge is

 A chain of length $L$ is placed on a horizontal surface as shown in figure. At any instant $x$ is the length of chain on rough surface and the remaining portion lies on smooth surface. Initially $x = 0$. A horizontal force $P$ is applied to the chain (as shown in figure). In the duration, $x$ changes from $x=0$ to $x=L$. For chain to move with constant speed,