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 ______ Youngs modulus is Y.

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

Answer 1

Answer: (A)

$\sqrt{\frac{2Tl^{2}}{4AY} + \frac{T^{2}l^{2}}{4A^{2}Y^{2}}}$

Answer 2

2T cos θ = W

or T = $\frac{W}{2\cos\theta}$

∆l = $\frac{Tl}{2AY}$δ = $\sqrt{\left( \frac{1}{2} + \Delta l \right)^{2} - \frac{l^{2}}{4}}$

or δ = $\sqrt{\left( \frac{1}{2} + \frac{Tl}{2AY} \right)^{2} - \frac{l^{2}}{4}} = \sqrt{\frac{2Tl^{2}}{4AY} + \frac{T^{2}l^{2}}{4A^{2}Y^{2}}}$