Question

A wire of length 10m and diameter 2mm elongates 0.2 mm when stretched by a weight of 0.55 kg. Calculate the Young's modulus of the material of the wire.
g = 9.8 ms^{-1}

Answer 1

Answer:

$\boxed{\underline{\underline{\Huge{\bold{8.58\times10^{10}}\bold{\:Nm}^\bold{-2}}}}}$

Explanation:

$L=10\text{ m};\:M=0.55\text{ kg};\:\:r=1\text{ mm}=1\times10^{-3}\text{ m};\:\:\:l=0.2\text{ mm}=2\times10^{-4}\text{ m}$

                   $Y = \dfrac{MgL}{\pi r^2l}=\dfrac{0.55\times9.8\times10}{\pi\times(1\times10^{-3})^2\times10^{-4}}\\= \dfrac{0.55\times9.8}{\pi\times2}\times10^{11}=\bold{8.58\times10^{10}}\bold{\:Nm}^\bold{-2}$