The system shown in the figure is released. Find the accelerations $a_1$ (for the $2 \ kg$ block) and $a_2$ (for the $3 \ kg$ block).

Imagine a situation in which the horizontal surface of block $M_0$ is smooth and its vertical surface is rough with a coefficient of friction $\mu$. Identify the correct statement$(s)$.

The frictional force acting on the $1 \,kg$ block is .................. $N$.

Determine the time in which the smaller block reaches the other end of the bigger block as shown in the figure. $(g = 10\ m s^{-2})$.

In the figure,the coefficient of friction between the floor and block $B$ is $\mu_1 = 0.2$ and between blocks $A$ and $B$ is $\mu_2 = 0.3$. The masses are $m_A = 20 \text{ kg}$ and $m_B = 40 \text{ kg}$. Find the maximum horizontal force $F$ that can be applied to block $B$ so that both blocks move together. (in $\text{ N}$)

Block $A$ of mass $2 \, kg$ is placed over block $B$ of mass $8 \, kg$. The combination is placed over a rough horizontal surface. The coefficient of friction between block $B$ and the floor is $0.5$. The coefficient of friction between blocks $A$ and $B$ is $0.4$. A horizontal force of $10 \, N$ is applied on block $B$. Find the force of friction between blocks $A$ and $B$. (Take $g = 10 \, ms^{-2}$)