$($A$)$

$($B$)$

The cantilever shown in Figure A has a square cross$-$section with a side length of $d=2mm($figure B$).$

If the density and the yield strength of the material that the bar is made of are $=3800kg{m}^{-3},$ and

${}_{\text{y}\text{i}\text{e}\text{l}\text{d}}=170$MPa, respectively, what is the maximum length, $L,$ of the bar that can be used in a

cantilever configuration without showing any plastic deformation? You should take the gravitational

acceleration as $g=9\mathrm{.}81m{s}^{-2}.$