Two masses $m_1$ and $m_2$ are placed on a smooth horizontal surface and are connected by a string of negligible mass. $A$ horizontal force $F$ is applied on the mass $m_2$ as shown in the figure. The tension in the string is

The figure shows three blocks in contact and kept on a smooth horizontal surface. What is the ratio of the force exerted by block $A$ on $B$ to that of $B$ on $C$?

Two blocks of mass $8\,kg$ and $2\,kg$ are connected by a string and they are released on an inclined plane of inclination $30^o$ as shown in the figure. What will be the tension in the string connecting the two blocks (in $,N$)? (Assume the surface is frictionless and $g = 10\,m/s^2$)

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 ............ $N$.

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 ........ $N$.

$A$ monkey of mass $40 \, kg$ climbs on a rope which can stand a maximum tension of $600 \, N$. In which of the following cases will the rope break: the monkey
$(a)$ climbs up with an acceleration of $6 \, m \, s^{-2}$
$(b)$ climbs down with an acceleration of $4 \, m \, s^{-2}$
$(c)$ climbs up with a uniform speed of $5 \, m \, s^{-1}$
$(d)$ falls down the rope nearly freely under gravity? (Ignore the mass of the rope).