$($a$)($i$)$ Find the buckling load of a $60cm20cm$ plate of thickness $3$ mm subject to compression in the $x-$direction. All the edges of the plate are simply$-$supported. Material used is aluminium with density $2\mathrm{.}7\frac{g}{c}{m}^3.$ If another plate $($made of steel$)$ of dimensions $60cm20cm$ is also given, what should be its thickness such that it resists the same amount of compression as the aluminium plate before buckling? Compare the weight of the $2$ plates. Steel density $7\mathrm{.}8\frac{g}{c}{m}^3.$

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