Question

A wire of length $L$ is clamped at two ends so that it lies horizontally and without tension. A weight $W$ is suspended from the middle point of the wire. The vertical depression is _______. (Young's modulus is $Y$.)

• A. $\sqrt{\frac{2T{l}^2}{4AY}+\frac{T^2{l}^2}{4A^2{Y}^2}}$
• B. $\sqrt{\frac{2T{l}^2}{4AY}-\frac{T^2{l}^2}{4A^2{Y}^2}}$
• C. $\sqrt{\frac{2T{l}^2}{4AY}}$
• D. $\frac{Tl}{2AY}$

Answer 1

The correct option is A $\sqrt{\frac{2T{l}^2}{4AY}+\frac{T^2{l}^2}{4A^2{Y}^2}}$

$2T\cos \theta =WorT=\frac{W}{2\cos \theta }\Delta l=\frac{Tl}{2AY}\delta =\sqrt{{(\frac{l}{2}+\Delta l)}^2-\frac{l^2}{4}}or\delta =\sqrt{{(\frac{l}{2}+\frac{Tl}{2AY})}^2-\frac{l^2}{4}}=\sqrt{\frac{2T{l}^2}{4AY}+\frac{T^2{l}^2}{4A^2{Y}^2}}$