Ncert Exercises & Solutions

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.

$∴ f = Mg . . . (i)$

$and F = N . . . (ii)$

$\begin{array}{l} But force of friction (f) = μN \\ = μF [using Eq . (ii)] . . . (iii) \\ From Eqs. (i) and (iii), we get μF = Mg \\ or F = \frac{Mg}{μ} \end{array}$

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