Question

6.A load of 1kg weight is attached to one end of a steel wire of cross sectional area 3mm2 and Young's modulus 10power11N/m2.The other end is suspended vertically from a hook on a wall then the load is pulled horizontally and released. when the load passes its lowest position the fractional change in length is
(g=10m/s2)

Answer 1

$$\begin{gathered} \mathrm{Force}\mathrm{acting}\mathrm{on}\mathrm{the}\mathrm{string}\mathrm{at}\mathrm{lowest}\mathrm{position}: \\ \mathrm{F}=\mathrm{mg}+2\mathrm{mg}=3\mathrm{mg} \\ \mathrm{Young}\text{'}\mathrm{s}\mathrm{modulus}: \\ \mathrm{Y}=\frac{\mathrm{FL}}{\mathrm{A}△\mathrm{L}} \\ \mathbf{Expression}\mathbf{}\mathbf{for}\mathbf{}\mathbf{fractional}\mathbf{}\mathbf{change}\mathbf{}\mathbf{in}\mathbf{}\mathbf{length}\mathbf{:} \\ \frac{△\mathrm{L}}{\mathrm{L}}=\frac{3\mathrm{mg}}{\mathrm{AY}} \\ =\frac{3\times 1\times 10}{3\times {10}^{-6}\times {10}^{11}} \\ \mathbf{=}{\mathbf{10}}^{\mathbf{-}\mathbf{4}} \end{gathered}$$