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A uniform cube of side ‘a’ and mass ‘m’ rest on a horizontal surface. A horizontal force F is applied normal to one face at a point that is directly above the centre of the face at a height $λ = \frac{3 a}{4}$ above the center. The minimum value of F for which the cube begins to topple above edge without sliding

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$\frac{m g}{4}$

$2 m g$

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

$\frac{m g}{2}$

answer is D.

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Detailed Solution

When cube is toppled about O

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

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