Question

A wire of diameter 2.5mm is streched by aforce 980N if the toung's modulus of the wire is 12.5×10raised to the power 10 Nper m square find the percentage increase in the length of the wire ​

Answer 1

Answer:- 0.16 %

Step by Step Solution:-

We have,

Young's modulus = 12.5 × 10¹⁰ N/m²

Diameter of  wire = 2.5 mm

Radius  of wire (r) = 2.5/2 = 1.25 mm = 1.25 × 10⁻³ m

Calculate cross section area of wire:-

A = πr²

A = π(1.25 × 10⁻³)² m²

A = 4.90 × 10⁻⁶ m²

Calculate Longitudinal Stress:-

Longitudinal stress is  defined as  force applied on unit  cross section area

Longitudinal Stress = F/A

                                = 980/(4.9× 10⁻⁶)  

                                =  200× 10⁶

                               = 2 × 10⁸ N/m²

We know that,

Longitudinal Strain = ΔL/L

Where ΔL is  change  in length and L is  initial length of  wire

Now,

Young's Modulus = Longitudinal Stress/Longitudinal Strain

12.5 × 10¹⁰   = 2 × 10⁸/(ΔL/L)

ΔL/L = 2×10⁸/12.5×10¹⁰

ΔL/L = 0.16  × 10⁻²

Now,

Percentage Increase in the length = ΔL/L × 100

                                                             =  0.16  × 10⁻² × 100

                                                             = 0.16 %