Question

If ρ is the density of the material of a wire and σ the breaking stress, the greatest length of the wire that can hang freely without breaking is :

• A. 2σ/ρg
• B. ρlσg
• C. ρg 2σ
• D. σ/ρg

Answer 1

Answer:

D. σ/ρg

Stress = (weight of wire) / Area

• Stress - σ
• weight of wire - mg
• Area - A

density = mass/volume

• ρ = m/V
• So, m = ρV

Substituting these values in stress equation,

• σ = (mg)/A
• σ = (ρVg)/A

Volume = Area x Height

• V = A x h
• σ = (ρVg)/A
• σ = (ρAhg)/A
• σ = ρhg

Rearranging this equation, we get

h = σ/ρg

Where, h indicates the greatest length of the wire that can hang freely without breaking.