A block $A$ of mass $2 \mathrm{kg}$ is placed over another block $B$ of mass $4 \mathrm{kg}$, which is placed over a smooth horizontal floor. The coefficient of friction between $A$ and $B$ is $0.4$. When a horizontal force of magnitude $10 \mathrm{N}$ is applied on $A$, the      acceleration of blocks $A$ and $B$ are 

Two blocks $m$ and $M$ tied together with an inextensible string are placed at rest on a rough horizontal surface with coefficient of friction $\mu$. The block $m$ is pulled with a variable force $F$ at a varying angle $\theta$ with the horizontal. The value of $\theta$ at which the least value of $F$ is required to move the blocks is given by

In the given figure, the tension in the rope (rope is light) is

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