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

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Here, mass of the block $=\mathrm{M}$

Coefficient of friction between the block and the wall $=\mu$

Lef $F$ be force required to hold the block against the wall.

Figure show that weight of block $\mathrm{mg}$ is in downward direction and frictional force is in upward direction.

For equilibrium

$\therefore f=\mathrm{Mg}$

$\mathrm{F}=\mathrm{N}$

Frictional force $f=\mu \mathrm{N}$

$=\mu \mathrm{F}$

Comparing $(1)$ and $(2)$,

$\mathrm{mF}=\mathrm{Mg}$

$\mathrm{F}=\frac{\mathrm{Mg}}{\mu}$

886-s185

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