Question

A cubical block of side $L$ and mass $m$ rests on a rough horizontal surface. A horizontal force $F$ is applied normal to one of its faces at a point that is directly above the centre of the face at a height $2L/3$ above the base. The minimum force $F$ required to topple the block before sliding is:

• A. $\frac{2mg}{3}$
• B. $\frac{3mg}{2}$
• C. $\frac{3mg}{4}$
• D. $\frac{4mg}{3}$

Answer 1

The correct option is C $\frac{3mg}{4}$

Toppling is phenomenon that generally happens when force is applied on a body of smaller base aera.

At the time of toppling the forces are acting as shown

Normal force shift to edge of block.

Taking moment about P

$F\times \frac{30}{4}=mg\left(9/2\right)$

$\Rightarrow F=\frac{2}{3}mg$