Given :

Young’s modulus Y for the wire = 12.5 x 10^{11} dyne cm^{-2}

=12.5 x 10^{10}Nm^{-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=πr^{2}=π(1.25 x 10^{-3})^{3} m^{2 }

Use the formula:Y=FL/A Δ L

Percentage inrease in length =ΔL/L x100

=(F/AY )x100

=(F/π r^{2}Y )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 % **