What will be the acceleration of the system and tension in the rope connecting $5\,kg$ and $1\,kg$ blocks?

The figure shows four blocks that are being pulled along a smooth horizontal surface. The masses of the blocks and the tension in one string are given. The pulling force $F$ is ............ $N$.

With what minimum acceleration can a fireman slide down a rope if the breaking strength of the rope is $\frac{2}{3}$ of his weight?

$A$ balloon of mass $M$ descends with an acceleration $a (< g)$. What mass needs to be removed from the balloon so that it starts ascending with acceleration $a$?

Three blocks of masses $3\, kg, 2\, kg$,and $1\, kg$ are placed side by side on a smooth surface as shown in the figure. $A$ horizontal force of $12\, N$ is applied to the $3\, kg$ block. The net force on the $2\, kg$ block is ............ $N$.

$A$ block of mass $1 \, kg$ is suspended by a string of mass $1 \, kg$ and length $1 \, m$ as shown in the figure. Taking $g = 10 \, m/s^2$,calculate the force exerted by the support on the string. (in $, N$)