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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.
Solution
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 $(2)$,
$\mathrm{mF}=\mathrm{Mg}$
$\mathrm{F}=\frac{\mathrm{Mg}}{\mu}$
