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Question: A Cu rod and a steel rod maintain a difference in their lengths constant = 10 cm at all temperatures...

A Cu rod and a steel rod maintain a difference in their lengths constant = 10 cm at all temperatures. If their coefficients of expansion are 1.6 × 10–5 K–1 and 1.2 × 10–5 K–1, then the length of the Cu rod is –

A

40 cm

B

30 cm

C

32 cm

D

24 cm

Answer

30 cm

Explanation

Solution

Dl1 = Dl2 Ž l1a1 DT = l2a2DT

Ž l1a1 = l2a2 Ž l2l1\frac{\mathcal{l}_{2}}{\mathcal{l}_{1}} = α1α2\frac{\alpha_{1}}{\alpha_{2}}Žl2l1\frac{\mathcal{l}_{2}}{\mathcal{l}_{1}}– 1=α1α2\frac{\alpha_{1}}{\alpha_{2}} – 1

l2–l1l1\frac{\mathcal{l}_{2}–\mathcal{l}_{1}}{\mathcal{l}_{1}} = α1–α2α1\frac{\alpha_{1}–\alpha_{2}}{\alpha_{1}} Ž l1 = α1(l2–l1)(α1–α2)\frac{\alpha_{1}(\mathcal{l}_{2}–\mathcal{l}_{1})}{(\alpha_{1}–\alpha_{2})}