Question

A steel rod of diameter 1 cm is clamped firmly at each end when its temperature is25 degree c so that it cannot contract on cooling the tension in the rod at 0 degree c is approximately

Answer 1

Explanation:

Given A steel rod of diameter 1 cm is clamped firmly at each end when its temperature is 25 degree c so that it cannot contract on cooling the tension in the rod at 0 degree c is approximately

• Given diameter = 1 cm = 10^-2 m
• Change in temperature is ΔT = 25 – 0
•                                                = 25
• Now young’s modulus Y = stress / strain
• Stress = y x strain
• Now alpha coefficient of linear expansion
• Strain = change in length / original length
•          = Δ l / l
•         = α Δ θ
• Now stress = Y α Δ θ
• We know that stress = force / unit area
• So Tension = Y A α Δ θ
•                  = Y π d^2 / 4 α Δ θ
•                  = 2 x 10^11 x 3.14 x 10^-4 x 10^-5 x 25 / 4
•                 = 3925 N

              ≅ 4000 N

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