Considering a simply supported beam subjecting to a point load $F$ at its mid$-$span. The span of the beam is denoted by $/$ and its cross section is a square of of side $t.$ The beam is made of a material with Young's modulus $E$ and density $p.$ Assume that the load is small so that the beam is deformed elastically.

Determine the mass of the beam in terms of $F,$I,$E,$ and the deflection of the beam at the mid$-$span $$

Given that $E=100$MPa,$l=0\mathrm{.}1m,F=50kN,$ density of $2400k\frac{g}{m}3,$ and a deflection of $2mm,$ compute the mass of the beam in unit of $kg.$

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