Question

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, what is the minimum force required to be applied by the finger to hold the block against the wall?

• A. $\mu Mg$
• B. Mg
• C. $\frac{Mg}{\mu }$
• D. $2\mu Mg$

Answer 1

The correct option is C $\frac{Mg}{\mu }$

Let F be the force applied by the finger on the block. N is the normal reaction of the wall on the block. Mg is weight of block acting vertically downwards. f is the force of friction between the wall and the block which acts upwards as shown in the figure.
The block will not fall, if
$f=Mg$
$\mu N=Mg$ ($\because f=\mu N$)
$\mu F=Mg(\because N-F)=F=\frac{Mg}{\mu }$