A uniform cube of side and mass m rests on a rough horizontal surface. A horizontal force F is applied normal to one face at point that is directly above the centre of the face at a height `(a)/(4)` above the centre. The minimum value of F for which the cube begins to topple above an edge without sliding is

Options

A. `(1)/(4)` mg
B. 2 mg
C. `(1)/(2)` mg
D. `(2)/(3)` mg

Answer

D

Explanation

For topping
`tau gt 0 `
`F {(3a)/(4)} - "mg" {(a)/(2)} gt 0 `
`F gt (2mg)/(3)`