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

\[\begin {array} {1 1} (a)\;\frac{2}{3}mg & \quad (b)\;\frac{4}{3}mg \\ (c)\;\frac{5}{4}mg & \quad  (d)\;\frac{1}{2}mg \end {array}\]

1 Answer

At the time of toppling the forces are acting as shown.
Normal force shift to the edge.
Taking moments about P
$F \times \large\frac{3a}{4}$$=mg \large\frac{a}{2}$
$F= \large\frac{2}{3} $$mg$
answered Dec 6, 2013 by meena.p

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