Physics - NLM Question with Solution | TestHub

For the block to remain stationary, the upward static friction force must balance the downward gravitational force. The normal force exerted by the wall on the block is equal to the applied horizontal force $F$. So, $N=F$. The maximum static friction force is $f_{s,max}={\mu }_{s}N={\mu }_{s}F$. For equilibrium, $f_s=mg$. To prevent falling, $f_{s,max}\ge mg$. Therefore, ${\mu }_{s}F\ge mg$, which implies $F\ge \frac{mg}{{\mu }_s}$. The minimum force is $\frac{mg}{{\mu }_s}$.