The steel wire of cross-sectional area 2 mm 2 [ Y = 200 GPa , α = 1 0 − 5 / ∘ C ] is stretched and tied firmly between two rigid supports, at a temperature = 2 0 ∘ C . At this moment, the tension in t

Question

The steel wire of cross-sectional area 2 mm 2 [ Y = 200 GPa , α = 1 0 − 5 / ∘ C ] is stretched and tied firmly between two rigid supports, at a temperature = 2 0 ∘ C . At this moment, the tension in the wire is 200 N . At what temperature will the tension become zero ?

TestHub · Accepted Answer

Heating reduces the tension. Tension is zero when thermal expansion cancels the initial stretch.

$200 = A Y α Δ T$

$200 = 2 \times 1 0^{- 6} \times 200 \times 1 0^{9} \times 1 0^{- 5} \times Δ T$

$200 = 4 Δ T \Rightarrow Δ T = 5 0^{\circ} C$

Final temperature $= 20 + 50 = 7 0^{\circ} C$

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