What is percentage increase in the length of a wire of diameter 2.5 mm stretched by a force of 100 kg wt?

Question

What is the percentage increase in the length of a wire of diameter 2.5 mm stretched by a force of 100 kg wt? Young's modulus of elasticity of the wire is 12.5 × 10^11 dyne / cm^2.

Answer 1

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)³ 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 10¹⁰ ] x 100

=15.96 x 10^-2=0.16 %

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