A load of 25 kg is attached to a of diameter 0.4 cm and a length of 100 cm of the wire is found to elongate to 102 cm. Find Young’s modulus for the material of the wire

Question

A load of 25 kg is attached to a of diameter 0.4 cm and a length of 100 cm of the wire is found to elongate to 102 cm. Find Young’s modulus for the material of the wire. [Ans. 0.975 × 10¹⁰ dyne/cm²]

Answer

Mass (m) = 25 kg

Original length (l) = 100 cm = 1 m

Force = m × g = 25 × 9.8 = 245 N

Diameter (d) = 0.4 cm = 0.4 × 10^-2 m

Change in length (Δl) = 102 – 100 = 2 cm or 0.02 m

Step 1: Calculation of Area

Area = πr²

= 22\over 7 × (0.2 × 10^-2)²

= 1.257 × 10^-5 m²

Step 2: Calculation of stress

Stress = Force \over Area

= 245 \over 1.257 × 10^{-5}

= 1.95 × 10⁷ N/m²

Step 3: Calculation of strain

Strain = Δl \over l

= 0.02 \over 1 = 0.02

Step 4: Calculation of Young modulus

Young modulus = stress \over strain

= 1.95 × 10^7\over 0.02

= 9.744 × 10⁸ N/m²

= 9.744 × 10^8 × 10^5 \over 10^{-4} dyne/cm²

= 0.975 × 10¹⁰ dyne/cm²