Three blocks of masses $4\, kg, 8\, kg$ and $24\, kg$ are connected to each other with light strings and placed on a smooth horizontal floor as shown in the figure. If the system moves with an acceleration of $2\, m/s^2$,the applied force $F$ is ............ $N$.

$A$ uniform thick string of length $8\, m$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $8\, N$ from one end. The tension in the string at $3\, m$ from the force applied is ........ $N$.

Two blocks of masses $5\, kg$ and $4\, kg$ are in contact with each other on a frictionless table. When a horizontal force of $9\, N$ is applied to the block of mass $5\, kg$,then the value of the force of contact between the two blocks is ........ $N$.

$A$ man slides down a light rope whose breaking strength is $\eta$ times the weight of the man $(\eta < 1)$. What is the maximum acceleration of the man so that the rope does not break?

$A$ uniform thick string of length $5\,m$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $5\,N$ from one end. The tension in the string at $1\,m$ from the force applied is ......... $N$.

$A$ trolley of mass $20 \ kg$ is attached to a block of mass $4 \ kg$ by a massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between the trolley and the surface is $0.02$,then the acceleration of the trolley and block system is (take $g=10 \ ms^{-2}$):- (in $ms^{-2}$)