A vertical $5m$ high column used in the structure of a system is made from an I section steel beam fixed to the foundation at the lower end. The I section is of depth $252mm,$ breadth $203mm,$ flange thickness $13\mathrm{.}5mm,$ and web thickness $8mm.$ The maximum allowable compressive stress in the steel is $150M\frac{N}{m^2}$ and the required safety factor on axial force against failure by buckling is $2.$ Find the maximum weight the column can support if $($a$)$ it is effectively free of constraint at its upper end, and $($b$)$ it is fixed at this end, with no lateral deflection allowed.