A composite rod is made by joining a copper rod end to end with a second rod of different material but of the same cross section. At 25º C the composite rod is 1 m in length of which the length of the copper rod is 30 cm. At 125º C the length of the composite rod increases by 1.91 mm. When the composite rod is not allowed to expand by holding it between two rigid walls it is found that the length of the two constituents do not change with the rise of temperature. Find the Young's modulus and the linear expansion of the second rod given that Young's modulus of for copper = 1.3 x 10 11 N/m 2 and the coefficient of linear expansion of copper = 1.7 x 10 -5 /º C.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(Y 2 = 1.105 x 10 11 N/m 2 , α 2 = 2 x 10 -5 /º C)
Sol. Δ λ = 1.91 mm = Δ λ 1 + Δ λ 2
⇒ 0.191 cm = λ 1 α 1 Δθ + λ 1 α 2 Δθ .
⇒ 0.191 = (30 × 17 × 10 –6 + 70 α 2 ) × 100
α 2 = 2 × 10 –5 Ans.
Y = 
F 1 = F 2
Y 1 A α 1 Δθ = Y 2 A α 2 Δθ .
∴ Y 2 = 
= 
= 1.105 x 10 11 N/m 2 Ans.
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