The brass rod is fixed at one end and free at the other end. If the length of the rod is \(L=2 \mathrm{~m}\), determine the greatest allowable load \(P\) that can be applied so that the rod does not buckle or yield. Also, determine the largest sidesway deflection of the rod due to the loading. \(E_{\mathrm{br}}=101 \mathrm{GPa}, \sigma_{Y}=69 \mathrm{MPa}\).

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P 10 mm 100 mm L B