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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 $\frac{3 a}{4}$ 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)

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$\frac{m g}{4}$

$\frac{3 m g}{4}$

$\frac{2 m g}{3}$

answer is A.

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Detailed Solution

To tilt about A, torque of F about A should be greater than torque of mg about A.

$F \frac{3 a}{4} \geq$ $m g \frac{a}{2}$ $\Rightarrow$ $F \geq \frac{2 m g}{3}$

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