For safety in climbing, a mountaineer uses a nylon rope that is 65 m long and 1.4 cm in diameter. When supporting a(n) 81-kg climber, the rope elongates 1.8 m. Find its Young's modulus.

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Young's modulus = stress /strain

Strain = 1.8/65

Stress = force/ area = mg/area

mg = 81*9.8 Newton

Area = (pi/4)*(1.4/100) m^2

Hence, stress = 81*9.8/(pi/4)*(1.4/100) = 5.1566*10^6 N/m^2

Hence, Young's modulus = 5.1566*10^6/(1.8/65) =186.211*10^6 N/m^2 Ans.

Area = (pi/4)*(1.4/100)^2 m^2

Hence, stress = 81*9.8/(pi/4)*(1.4/100)^2 = 5.1566*10^6 N/m^2

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