Question

A regular hexagonal uniform block of mass $m=4\sqrt{3}\text{kg}$ rests on a rough horizontal surface with coefficient of friction $\mu$ as shown in figure. A constant horizontal force is applied on the block as shown. If the friction is sufficient to prevent slipping before toppling, then the minimum force (in $\text{N}$) required to topple the block about its corner $\text{A}$ is
(Take $g=10{\text{m/s}}^2$)

Answer 1

Situation when the hexagonal block is just about to topple. Normal reaction will shift to $\text{A}$ (extreme)


Torque balance about point $\text{A}$ :
$F\left(2a\cos {30}^o\right)=mg\left(\frac{a}{2}\right)$
$F(2\times a\times \frac{\sqrt{3}}{2})=4\sqrt{3}\times 10\times \frac{a}{2}$
$F=20\text{N}$