A uniform wire of length l and weight w is su | vedclass

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(B) The stress at any point in a wire is defined as the total force acting on the cross-section at that point divided by the area $A$.At a distance $x

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$2$/$3$

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(B) The stress at any point in a wire is defined as the total force acting on the cross-section at that point divided by the area $A$.At a distance $x$ from the top,the total weight supported by the cross-section consists of the weight $W$ at the bottom plus the weight of the portion of the wire below that point.The length of the wire below the point at distance $l/3$ from the top is $l - l/3 = 2l/3$.Since the wire is uniform,the weight of this portion is $w' = w \cdot (2l/3) / l = 2w/3$.The total force at this cross-section is $F = W + 2w/3$.The stress is $\sigma = F/A = (W + 2w/3) / A = W/A + (2/3)(w/A)$.Comparing this with the given expression $(W/A + \gamma \cdot w/A)$,we find that $\gamma = 2/3$.

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