Answer: The steel wire will stretch up to 1837.5 mm
Explanation:
We are given:
Mass = 25 kg
Length of wire = 10 m
Area of cross-section of wire = [tex]1.5\times 10^{-4}cm^2=1.5\times 10^{-8}m^2[/tex] (Conversion factor: [tex]1cm^2=10^{-4}m^2[/tex] )
To calculate the change in stretching, we use the equation:
[tex]E=\frac{Fl}{A\Delta l}[/tex]
where,
E = young modulus of steel = [tex]20\times 10^{10}Pa[/tex]
F = force exerted by the weight = m g = [tex]25kg\times 9.8m/s^2[/tex]
l = length of wire = 10 m
A = area of cross section = [tex]1.5\times 10^{-8}m^2[/tex]
[tex]\Delta l[/tex] = change in length = ?
Putting values in above equation, we get:
[tex]20\times 10^{10}=\frac{25\times 9.8\times 10}{1.5\times 10^{-8}\times \Delta l}\\\\\Delta l=1.8375m[/tex]
Converting above value in mili meters, we use the conversion factor:
1 m = 1000 mm
So, 1.8375 m = 1837.5 mm
Hence, the steel wire will stretch up to 1837.5 mm
