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A uniform cube of side a and mass m rest...

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?

Text Solution

Verified by Experts

In the limiting case normal reaction will pass through `O`. The cube will torque about `O` if torque of `F` exceeds the torque of `mg`.

`rArrF((3a)/4)gtmg(a/2), rArrFgt2/3 mg`
So, the minimum value of `F` is `2/3 mg`
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