Question

A uniform cube of side $a$ and mass $m$ rests on a horizontal table. A horizontal force ${}^{\prime }{F}^{\prime }$ 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 ${}^{\prime }{F}^{\prime }$ 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 $\frac{2}{3}mg$

At the condition of just begins to tilt, normal reaction of the cube will shift to its edge as shown.


(Figure shows the situation when the cube is just about to tilt)
At this condition, net torque about point $P=0$ (for minimum force $F$)
i.e $F\times \left(\frac{3a}{4}\right)=mg\times \left(\frac{a}{2}\right)$
$\therefore F=\frac{2mg}{3}$