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.

Explanation

Given , mass of the block = M
Coefficient of friction between the block and the wall = `mu`
Let a factor F be applied on the block to hold the block against the wall . The normal reaction of mass be N and force of friction acting upward be f in equilibrium , vertical and horizontal forces should be balanced separately.
`therefore " " f = Mg " " .......(i)`
and `" " F = N " " .....(ii)`

But force of friction (f) = `mu N`
= `mu F " " ["using Eq." (ii) - (iii)`]
From Eqs. (i) and (iii) , we get `mu F = Mg`
or `" " F = (Mg)/(mu)`