The young's modulus is E = 1.4938211 × [tex]10^5 N/m^2[/tex]
The length of the rope is, L = 65 m.
The diameter of the rope is, d = 1.2 cm = 0.012 m.
The mass of climber is, m = 80 kg.
Given elongation of rope = Δ L = 1.4 m
Young's Modulus of Material is the product of the ratio of stress to strain produced in a material. Then,
E = σ /ε
E = W / A / L/ ΔL
E = ( mg × Δ L ) ÷ (π/4 × d² ×L )
On substituting the values we get ;
( take g = 9.8 m/s^2)
E = 1097.6 / 0.0073476
E = 149,382.11 [tex]N/m^2[/tex]
E = 1.4938211 × [tex]10^5 N/m^2[/tex]
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