A copper rod of crosssectional area 0.500 cm2 and length 1.00 m is elongated by 2.00 * 10-2 mm and a steel rod of the same cross-sectional area but 0.100 m in length is elongated by 2.00 * 10-3 mm. Which rod is under greater tensile strain?

The rod under greater tensile strain is ; Neither of them i.e. They both have the same tensile strain

Given data :

Cross sectional area of copper rod = 0.5 cm²

Length of copper rod  = 1.0 m  = 1 * 10³ mm

Elongation of copper rod ( Ec )  = 2.0 * 10⁻² mm

For Steel

Cross sectional area of steel = 0.5 cm²

Length of steel rod = 0.1 m  = 1 * 10² mm

Elongation of steel rod  ( Es )=  2.0 * 10⁻³ mm

Determine the Tensile strain of each rod

i) For copper rod

Tensile strain = Ec / Length of copper rod

                       = ( 2.0 * 10⁻² ) /  ( 1 * 10³ )

                       = 2.0 * 10⁻⁵

ii) For the steel rod

Tensile strain = Es / Length of steel rod

                       = ( 2.0 * 10⁻³ ) / ( 1 * 10² )

                        = 2.0 * 10⁻⁵

The Tensile strain for the copper rod and the steel rod is the same ( 2.0 * 10⁻⁵ ) This means that both rods are under the same tensile strain

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Explanation:

Strain of a material is the ratio of its extension to its original length.

strain = e/lo

e is the extension

lo is the original length

For a copper rod;

e = 2.00 * 10^-2mm

lo = 1.00m

convert 1.00m to mm

1.00m = 1*10^-3mm

get the strain

Strain = 2.00 * 10^-2mm/1*10^-3mm

Strain = 2 * 10^{-2+3}

Strain = 2*10^1 = 20

For the steel

e = 2.00 * 10^-3mm

lo = 0.100m

convert 0.100m to mm

0.1m = 0.1*10^-3mm

0.1m = 10^-4mm

get the strain

Strain = 2.00 * 10^-3mm/10^-4mm

Strain = 2 * 10^{-3+4}

Strain = 2*10^1 = 20

Since the value of their strain are the same, this means that they a re under the SAME tensile strain. No one is greater that the other.

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