AIIMS 2018 Physics Stress and Strain MCQ Question

To determine the length of the wire that will break under its own weight, we use the formula for stress, which is defined as force per unit area (σ = F/A). The force due to the weight of the wire is given by F = ρgL, where ρ is the density, g is the acceleration due to gravity, and L is the length of the wire. Setting the stress equal to the breaking stress (6×10⁶ Nm⁻²), we can solve for L:

$$L = \frac{σA}{ρg} = \frac{6×10⁶ \, \text{N/m}² \cdot A}{3×10³ \, \text{kg/m}³ \cdot 10 \, \text{m/s}²} = 200 \, \text{m}.$$

Options A (20 m), C (100 m), and D (2000 m) do not satisfy the condition for breaking under the weight of the wire, as they yield stress values below the breaking limit.