A vertical hanging bar of length l and mass m | vedclass

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(B) Tensile stress is defined as the ratio of the tension force at a point to the cross-sectional area $A$ of the bar.At a distance $x$ from the top s

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$\frac{Mg + mg(l-x)}{A}$

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(B) Tensile stress is defined as the ratio of the tension force at a point to the cross-sectional area $A$ of the bar.At a distance $x$ from the top support,the tension in the bar is equal to the total weight acting below that point.The length of the bar below the point at distance $x$ is $(l-x)$.The mass of this portion of the bar is $m 	imes (l-x)$.The weight of this portion is $mg(l-x)$.The load $M$ at the bottom also contributes to the tension,with a weight of $Mg$.Therefore,the total tension $T$ at distance $x$ is $T = Mg + mg(l-x)$.The tensile stress $\sigma$ is given by $\sigma = \frac{T}{A} = \frac{Mg + mg(l-x)}{A}$.

$A$ vertical hanging bar of length $l$ and mass $m$ per unit length carries a load of mass $M$ at its lower end. Its upper end is clamped to a rigid support. The tensile stress at a distance $x$ from the support is (where $A$ is the area of cross-section of the bar):

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