Two blocks $A$and $B$of the same mass are joined by a light string and placed on a horizontal surface. An external horizontal force $F$ acts on $A$. The tension in the string is $T$. The forces of friction acting on $A$ and $B$ are $f_1$ and $f_2$ respectively. The limiting value of $f_1$ and $f_2$ is f. As $F$ is gradually increased:

$(a, b, c)$ For $F < f$, the block $A$ will not move and so $T = 0$

         For $f < F > 2f$, the block $A$ has tendency of motion, and so string becomes tight, then

         $F = T + f \Rightarrow T = F – f$

For $F > 2 f$, both the blocks start moving with constant acceleration,

         $a = \frac{F-2f}{2m}$

Now        $T – f = ma$

or           $T-f = \frac{F-2f}{2m}$

           $T = F/2$