Q. 30 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 μ 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.

Hint: Balance the forces.
Step 1: Write the equation in horizontal and vertical directions
Given, the mass of the block = M
Coefficient of friction between the block and the wall = μ
Let a force F be applied on the block to hold the block against the wall. The normal reaction of mass is N and the force of friction acting upward be f. In equilibrium, vertical and horizontal forces should be balanced separately.
 
               f = Mg              ...(i)
and            F = N                ...(ii)
 
 
 But force of friction (f)=μN                                      = μF               using Eq. ii               ...iii From Eqs. (i) and (iii), we get μF=Mg or F=Mgμ