Calculate the Young’s modulus for the wire of cross-sectional area 6×10-5 m2 and length 50 cm which stretches by 0.2 mm under a load of 3000N.
Young's modulus is calculated using the formula:
Young's modulus (Y) = (stress / strain)
where stress is the force applied per unit area and strain is the change in length of the wire divided by its original length.
We need to calculate stress and strain first.
Given:
Cross-sectional area (A) = 6 × 10^(-5) m^2
Original length (L) = 50 cm = 0.5 m
Change in length (ΔL) = 0.2 mm = 0.0002 m
Force applied (F) = 3000 N
Stress (σ) = Force (F) / Area (A)
= 3000 N / 6 × 10^(-5) m^2
= 5 × 10^7 N/m^2
Strain (ε) = Change in length (ΔL) / Original length (L)
= 0.0002 m / 0.5 m
= 0.0004
Now, we can calculate Young's modulus:
Young's modulus (Y) = Stress (σ) / Strain (ε)
= (5 × 10^7 N/m^2) / 0.0004
= 1.25 × 10^11 N/m^2
Therefore, the Young's modulus for the given wire is 1.25 × 10^11 N/m^2.