Question

A cubical block of 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 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. $\frac{mg}{2}$
• B. $\frac{mg}{4}$
• C. infinitesimal
• D. $mg(1-\mu )$

Answer 1

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


$\therefore$ Clearly, the block shall topple about its edge through $O$.

The torque $FL$ of the applied force is clockwise. The torque $\frac{mgL}{2}$ of the weight is anti-clockwise.
Applying condition for rotational equilibrium -
$FL-mg\frac{L}{2}=0$

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

$\therefore \left(c\right)$