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 face 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 topple about an edge?

A uniform cube of side a and mass m rests on a rough horizontal table.

1.	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 face 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 topple about an edge?
Answer» Solution :In the LIMITING cse normal REACTION will pass through 0. The cube will topple about O if torque of F ecceeds the torque of mg. `impliesF((3a)/(4))gtmg((a)/(2))` `impliesFgt(2)/(3)mg` So, the MINIMUM value of F is `(2)/(3)` mg