Question

Calculate the percentage increase in length of a wire of diameter 2.5 mm

Answer 1

Calculate the percentage increase in the length of a wire of diameter 2.5 mm stretched by a force of 100 kg f if Young’s modulus Y for the wire = 12.5 x 10¹¹ dyne cm⁻²

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Answers

prmkulk1978

prmkulk1978 Ace

Given :

Young’s modulus Y for the wire = 12.5 x 10¹¹ dyne cm⁻²

=12.5 x 10¹⁰Nm⁻²

Diameter =D=2.5mm=2.5 x 10⁻³ m

Force=F=100kg f

=100x 9.8N

=980N

Formula to be used :ΔL/Lx100

A=πr²=π(1.25 x 10⁻³)² m²

Use the formula:Y=FL/A Δ L

Percentage inrease in length =ΔL/L x100

=(F/AY )x100

=(F/π r²Y )x100

=[980/3.142 x (1.25 x 10⁻³)² x 12.5 x 10 ¹⁰ ] x 100=15.96 x 10⁻²=0.16 %

∴The percentage increase in the length of a wire is 0.16 % .