A) \[\frac{WL}{2AY}\]
B) \[\frac{2WL}{AY}\]
C) \[\frac{WL}{AY}\]
D) \[\frac{WL}{4AY}\]
Correct Answer: A
Solution :
Consider a small length \[dx\] of the rod at distance \[x\] from the fixed end. The part below this small element has length\[L-x\]. The tension T of the rod at the element equals the weight of the rod below it. \[T=(L-x)\frac{W}{L}\] Elongation in the element is given by elongation = original length \[\times \] stress/Y The total elongation\[-\int\limits_{0}^{L}{\frac{(L-x)W\,dx}{LAY}=}\]\[\frac{W}{LAY}\left( Lx-\frac{x}{2} \right)_{0}^{L}=\frac{WL}{2AY}\]You need to login to perform this action.
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