A horizontal force F pushes wedge of mass M on a smooth horizontal surface. A block of mass m is stationary relative to the wedge, then :

As block of mass m is stationary relation to wedge frictional force must be equal to ‘mg’

$\text{F}=\text{mg}\to \left(1\right)$

$\text{N}=\text{ma}$

$\mu \text{N}=\text{mg}$

$\mu \text{ma}=\text{mg}$

$\mu \text{a}=\text{g}$

$\mu \times \frac{\text{F}}{\text{M}+\text{m}}=g\to \left(2\right)$

$\mu =\frac{\left(\text{M}+\text{m}\right)\text{g}}{\text{F}}\text{using}\text{eq}\left(2\right)$

$\text{F}=\frac{\left(\text{M}+\text{m}\right)\text{g}}{\mu }$

The relation

$\text{N}=\text{ma}=\frac{\text{mF}}{\left(\text{M}+\text{m}\right)}$