Placed on a smooth horizontal table, two blocks of equal mass m are...

Let the acceleration of the system be $a$.

The total mass of the two blocks is $m + m = 2m$.

Since a constant force $F$ is applied to the system, the acceleration is given by Newton's second law:

$a = \dfrac{F}{2m}$

Let $T$ be the tension in the string. The only horizontal force acting on the trailing block of mass $m$ is the tension $T$.

The equation of motion for the trailing block is:

$T = ma$

Substituting the value of $a$ into the equation:

$T = m \left(\dfrac{F}{2m}\right) = \dfrac{F}{2}$