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

1.	A uniform cube of slide 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 O. The cube will TOPPLE about O if torque of F ecceeds the torque of MG. `rArr F((3a)/(4))gt mg((a)/(2)), rArr F gt (2)/(3)mg` So, the minimum value of F is `(2)/(3)mg`.