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`
B. `(mg)/3`
C. `(2mg)/3`
D. `(5mg)/3`

Answer

C

Explanation

In the limiting case normal reaction will pass through `O`. The cube will tip about O if torque of `F` exceeds the torque of
`mg`.
Hence, `F((3a)/(4))gtmg((a)/(2))`
or `Fgt(2)/(3)mg`
Therefore, minimum value of `F` is `(2)/(3)mg`.