In the previous problem, if the coefficient of friction is `mu`, find whether the box will slide first or topple.
(a) If the box is of height `h` having square base measuring `axxa`.
(b) If the box is hollow cylinder of radius `r` and height `h`.

Explanation

(`a`)
(`i`) For tipping over `A` (torque about `O`)
`fxx(h)/(2)gtNxx(a)/(2)`
`mgsintheta(h)/(2)gtmgcostheta(a)/(2)`
`tanthetagt(a)/(h)`
(`ii`) For sliding
`mgsinthetagtf_(max)(=mumgcostheta)`
`tanthetagtmu`
The box will slide before topple if `mult(a)/(h)`
(`b`)
When the cylinder is at rest
`N=mgcostheta,f=mgsintheta`
The cylinder will topple if
`fxx(h)/(2)gtNxxr` (torque about the center of mass `O`)
`mgsintheta (h)/(2)gtmgcosthetaxxr`
`tanthetagt(2r)/(h)`
The cylinder will slide if
`mgsinthetagtf_(max)` (`=mumgcostheta`)
`tanthetagtmu`
The cylinder will slide before topple if `mult2r//h`.
The cylinder will topple before slide if `mugt2r//h.`