Stress is defined as the force applied per unit area. In the context of a wire being loaded by a weight, the weight acts as the force exerted, and the cross-sectional area of the wire is the area over which this force is distributed.
Force (F): This is given by the weight, which is y2 N.
Cross-sectional Area (A): For a wire with a diameter, the area can be calculated using the formula for the area of a circle: A = πr2, where r is the radius of the wire.
Given the diameter of the wire as yπ meters, the radius (r) is half of the diameter:
r = (yπ)/2
So, the area (A) is:
A = π[(yπ)/2]2
Simplifying the area:
A = π(y2π2/4)
A = y2π3/4
Stress (σ) is given by the formula:
σ = F/A
Substituting the given weight (force) and the calculated area:
σ = (y2) / (y2π3/4)
By simplifying the expression:
σ = (4y2) / (y2π3)
Cancel out y2 from numerator and denominator:
σ = 4/π2 Nm−2
Thus, the correct stress experienced by the wire is 4π Nm−2, as provided in one of the options. The explanation shows clearly how the force and area are used to derive the stress experienced by the wire.