$A$ block of mass $M$ is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is $\mu$ and the acceleration due to gravity is $g$,calculate the minimum force required to be applied by the finger to hold the block against the wall.

(D) Given:
Mass of the block $= M$
Coefficient of friction between the block and the wall $= \mu$
Let $F$ be the force applied by the finger to hold the block against the wall.
The forces acting on the block are:
$1$. Weight $Mg$ acting vertically downwards.
$2$. Applied force $F$ acting horizontally towards the wall.
$3$. Normal reaction $N$ from the wall acting horizontally away from the wall.
$4$. Frictional force $f$ acting vertically upwards to oppose the downward motion.
For the block to be in equilibrium:
Vertical direction: $f = Mg$
Horizontal direction: $F = N$
We know that the maximum frictional force is $f = \mu N$.
Substituting $N = F$,we get $f = \mu F$.
To hold the block,the frictional force must balance the weight:
$\mu F = Mg$
$F = \frac{Mg}{\mu}$