Question

A uniform wire of length $1m$ and radius $0.028cm$ is employed to raise a stone of density $2500kg/m^3$ immersed in water. Find the change in elongation of wire when the stone is raised out of water. $[massofstone=5kg,Yofmaterialofwire=2\times {10}^{11}N/m^2]$

Answer 1

When a stone is raised from water wright increases as the buoyant force extingushes i.e., the change in force equal to the buoyant force being applied by water an the stone.

As buoyant force

$F_L=l_{f}Vg$ where, $l_f=$density of displaced field

$F_b=1000\times \left(\frac{5}{2500}\right)\times V=$ volume of field displaced $[l_f=1000kg/m^3]$

$F_b=2g$

then, bu Youngls modulus

$Y=\frac{F/A}{\Delta l/l}$

$2\times {10}^{11}=\frac{2g/\pi (0.00028{)}^2}{\Delta l/1}$

$2\times {10}^{11}=\frac{2g}{\pi \times {28}^2\times {10}^{-10}\Delta l}$

$\Delta l=\frac{2g}{\pi \times {10}^{11}\times \pi \times {28}^2{10}^{-10}}$

$\Delta l=\frac{2\times 10}{2\times \pi \times {28}^2\times 10}$

$\Delta l=\frac{1}{\pi \times {28}^2}$

$\Delta l=4.06\times {10}^{-4}m$

$\Delta l=0.0406cm$

Thus, the wire elongates by $0.0406cm$ in raising the rock from water.