A cubical box rests on a rough, horizontal, rectangular plank of friction coefficient `(1)/(sqrt3)`. Now the plank is slowly raised so that it makes some angle with horizontal. Find whether the box will slide first or topple.

Explanation

When the box is about to topple, normal reaction will pass through the point `A`

Let `a` be the side of the cube.
The box will topple if (torque about `O`)
`fxx(a)/(2)gtNxx(a)/(2)`
`fgtN`
`mgsinthetagtmgcostheta`
`tanthetagt1 implies thetagt45^(@)`
The box will slide if
`mgsinthetagtf_(max)` (`=muN=mumgcostheta)`
`tanthetagtmu(=(1)/(sqrt3))`
`thetagt30^(@)`
The box will slide first and then topple.