A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal face 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 face 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 ESE normal REACTION will PASS through O. The cube will topple about O if torque of F ecceeds the torque of mg. `impliesF((3a)/(4)) GT mg ((a)/(2))` `impliesF gt (2)/(3)mg` So, the minimum value of `F` is `(2)/(3)mg`