$A$ force of $0.5 \ N$ is applied on the upper block as shown in the figure. The coefficient of static friction between the two blocks is $0.1$ and that between the lower block and the surface is zero. The work done by the lower block on the upper block for a displacement of $3 \ m$ of the upper block is ...... $J$.

Two blocks $(A)$ of $2\,kg$ and $(B)$ of $5\,kg$ rest one over the other on a smooth horizontal plane. The coefficient of static and dynamic friction between $(A)$ and $(B)$ is the same and equal to $0.60$. Find the maximum horizontal force that can be applied to $(B)$ such that both $(A)$ and $(B)$ do not have any relative motion. $(g = 10\,m/s^2)$

$A$ truck of mass $8 \text{ ton}$ is carrying a block of mass $2 \text{ ton}$. If a breaking force of $25 \text{ kN}$ is applied on the truck, then the frictional force acting on the block is (Coefficient of static friction between the block and the truck is $0.3$) (in $\text{ N}$)

If $100 \,N$ force is applied to $10 \,kg$ block as shown in the diagram,the acceleration of $40 \,kg$ slab is (in $\,ms^{-2}$)

The maximum acceleration of the $5\, kg$ block is ...... $m/s^2$.

Two blocks ($m = 0.5\, kg$ and $M = 4.5\, kg$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac{3}{7}$. Find the maximum horizontal force $F$ that can be applied on the larger block so that the blocks move together. (Round off to the nearest integer) [Take $g = 9.8\, m/s^2$]