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 directly above the centre of the face, at a height `(3a)/(4)` above the base. What is the minimum value of `F` for which the cube begins to tip about an edge?

Options

A. `(Mg)/3`
B. `2/3 mg`
C. `Mg`
D. `(Mg)/(sqrt(2))`

Answer

B

Explanation

Talking moments about of point O

Moment of N (normal reaction) and f (force of friction) are zero. In critical case normal reaction will pass through O. the tip about the edge, moment of F should be greater than moment of mg or, `F=((3a)/4) gt (mg)a/2`
`F gt 2/3 mg`