Question

A cubical block of mass $m$ and side $L$ rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force $F$ is applied on the block as shown in the figure. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is:

• A. $\frac{mg}{4}$
• B. $\frac{mg}{8}$
• C. $\frac{mg}{2}$
• D. $mg(1-\mu )$

Answer 1

The correct option is C $\frac{mg}{2}$

Considering case 1, when minimum force is applied,
$F=\mu N$
$N=mg$
$\therefore F=\mu mg$
Now,
when the force exceeds some value, block topples
Taking $\sum$ moment about the toppling axis,

$\sum M=0$ ................ Still in equilibrium

$\therefore \sum M=\sum F.d$

$\Rightarrow 0=F\times L-mg\times \frac{L}{2}$

$\therefore F=\frac{mg}{2}$