The breaking stress of steel is 7.9×10⁹ Nm^–2 and density of steel is 7.9×10³ kgm^–3 and g = 10ms^–2. The maximum length of steel wire that can hang vertically without breaking is

Given:

• Breaking stress of steel (σ): 7.9 × 10⁹ N/m²
• Density of steel (ρ): 7.9 × 10³ kg/m³
• Gravitational acceleration (g): 10 m/s²

Solution:

Formula:

The breaking stress is the force per unit area. For a vertical hanging wire, the force due to gravity acting on the wire is:

F = Weight of the wire = mass × g = ρ × A × L × g

where:

• A = cross-sectional area of the wire (in m²),
• L = length of the wire (in meters),
• ρ = density of steel (in kg/m³),
• g = gravitational acceleration (in m/s²).

Since the stress is defined as force per unit area, we can equate the stress to the breaking force divided by the area:

σ = F / A = (ρ × A × L × g) / A

After simplifying, we get:

σ = ρ × L × g

Solving for the length (L):

L = σ / (ρ × g)

Substituting the given valu L = 7.9 × 10⁹ / (7.9 × 10³ × 10) = 7.9 × 10⁹ / 7.9 × 10⁴ = 10⁵ meters Final Answer

The maximum length of the steel wire that can hang vertically without breaking is 10⁵ meters.