Question

Find stress, strain and Young modulus of elasticity in the case of a wire $1.5m$ long & $1mm$ in cross section, if it is increased by $1.55mm$ in length when a weight of $10kg$ is suspended from it.

Answer 1

Given that,

Length of the wire$l=1.5m$

Change in length $\Delta l=1.55\times {10}^{-3}m$

Weight = $m=10kg$

Now, the stress is

$=\frac{F}{A}$

$=\frac{mg}{A}$

$=\frac{10\times 10}{0.785\times {10}^{-6}}$

$=127.3\times {10}^{6}N/m^2$

Now, the strain is

$=\frac{\Delta l}{l}$

$=\frac{1.55\times {10}^{-3}}{1.5}$

$=1.03\times {10}^{-3}$

Now, the young modulus is

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

$Y=\frac{127.3\times {10}^6}{1.03\times {10}^{-3}}$

$Y=123.5\times {10}^9$

$Y=1.23\times {10}^{11}N/m^2$

Hence, the stress, strain and young modulus is $127.3\times {10}^{6}N/m^2,1.03\times {10}^{-3},1.23\times {10}^{11}N/m^2$