A block of mass m is positioned on another block of mass M , and...

Given that the two blocks move together, they share the same acceleration. The acceleration of the system is given by:

$a = \dfrac{F}{2(m+M)}$

For the smaller block of mass $m$, the only horizontal force acting on it is the static frictional force $f$ provided by the lower block. This frictional force is responsible for its acceleration.

Applying Newton's second law to the smaller block:

$f = ma$

Substituting the value of acceleration $a$ into the equation, we get:

f = m \left[\dfrac{F}{2(m+M)} \right]

$f =$\dfrac{mF}{2(m+M)}