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 $\frac{3a}{4}$ above the base. The minimum value of 'F' for which the cube begins to tilt about the edge is (assume that the cube does not slide).

• A. $\frac{2}{3}$mg
• B. $\frac{4}{3}$mg
• C. $\frac{5}{4}$mg
• D. $\frac{1}{2}$mg

Answer 1

The correct option is A $\frac{2}{3}$mg

The minimum force for which cube begins to tilt, the normal reaction should pass through the tilting edge point 'O'.

Taking moments about point O,

$F\times \frac{3a}{4}=mg\times \frac{a}{2}$

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