Question

For the given dimensions shown in figure, find critical value of coefficient of friction $\mu$.

• A. ${\mu }_{cr}=2$
  
• B. ${\mu }_{cr}=\frac{1}{2}$
• C. ${\mu }_{cr}=\frac{3}{2}$
• D. ${\mu }_{cr}=\frac{2}{3}$

Answer 1

The correct option is B ${\mu }_{cr}=\frac{1}{2}$

Given,
mass of block$=m$,

Condition of sliding: The block will slide if,
$F>\mu N$

free body diagram, $N=mg$

$\therefore F>\mu mg....\left(1\right)$

Condition of toppling:
Block will topple about an axis passing through $\text{O}$ and perpendicular to plane of paper if:

clockwise torque of $F>$ anticlockwise torque of $mg$

$F\left(2a\right)>\left(mg\right)\left(a\right)$

$\therefore F>\frac{1}{2}mg....\left(2\right)$

From Eqs. (1) and (2), we can see that,

$\therefore {\mu }_{cr}=\frac{1}{2}$

Hence, option (b) is the correct answer.