A load of 4.0 kg is suspended from a ceiling through a steel wire of length 2.0 m and radius 2.0 mm. It is found that the length of the wire…

Young’s modulus (Y) measures how stiff a material is. The formula is:

Y = (F × L) / (A × e)

where F = force (weight of load), L = original length, A = cross-sectional area of the wire, and e = extension (increase in length).

Step 1: Find the force (F).
F = mg = 4.0 × 9.8 = 39.2 N

Step 2: Convert units.
L = 2.0 m
r = 2.0 mm = 2.0 × 10⁻³ m
e = 0.031 mm = 0.031 × 10⁻³ m = 3.1 × 10⁻⁵ m

Step 3: Find the cross-sectional area (A).
A = πr² = π × (2.0 × 10⁻³)² = π × 4.0 × 10⁻⁶ = 1.257 × 10⁻⁵ m²

Step 4: Calculate Young’s modulus.
Y = (39.2 × 2.0) / (1.257 × 10⁻⁵ × 3.1 × 10⁻⁵)
Y = 78.4 / (3.897 × 10⁻¹⁰)
Y = 2.01 × 10¹¹ Nm⁻²

So Young’s modulus of the steel wire is approximately 2 × 10¹¹ Nm⁻².