Question

A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face, at a height $3a/4$ above the base. The minimum value of $F$ for which the cube begins to tip about the edge is ............... (Assume that the cube does not slide)

Answer 1

$ForminimumFthetorqueofFaboutthetopplingpointshouldbeequaltothetorqueofweight.F\left(\frac{3a}{4}\right)=mg\left(\frac{a}{2}\right)\Rightarrow F=\frac{2}{3}mg$