Question

A steel wire of 5.65 mm diameter and 50 m length is used for a hoisting crane. The wire is used to vertically lift a weight of 200 kg attached to its lowest end. Assume the Young's Modulus of Elasticity of Steel as \(2 \times 10^5 \, \text{N/mm}^2\) and gravitational acceleration as \(10 \, \text{m/sec}^2\). The elongation of the steel wire (in mm) will be ............ [rounded off to two decimal places].

Hint:

For elongation problems: 1. Always use consistent units (mm for length, mm\(^2\) for area, N/mm\(^2\) for modulus). 2. Cross-sectional area of wire is \(\pi d^2/4\). 3. Formula: \(\Delta L = \dfrac{PL}{AE}\) is the fundamental relation from Hooke's law.