Question

A wire of length $3m$, diameter $0.4mm$ and Young's modulus $8\times {10}^{10}N/m^2$ is suspended from a point and supports a heavy cylinder of volume ${10}^{-3}{m}^3$at its lower end. Find the decrease in length (in mm) when the metal cylinder is immersed in a liquid of density $800kg/m^3$.

Answer 1

If $\Delta l$ be the decrease in length, $\Delta l=\frac{Fl}{AY}$

Here $F=upthrust=mg=\rho Vg$ and $F=\pi r^2$

$\Delta l=\frac{\rho Vgl}{\left(\pi r^2\right)Y}=\frac{800\times {10}^{-3}\times 9.8\times 3}{3.14\times (0.2\times {10}^{-3}{)}^2\times 8\times {10}^{10}}=2.34\times {10}^{-3}m$