A copper rod and a steel rod maintain a difference in their lengths of 10 c m at all temperatures. If their coefficients of expansion are 1.6 × 1 0 - 5 K - 1 ⁡ and 1.2 × 1 0 - 5 K - 1 ⁡ , then the length of the copper rod is

Question

A copper rod and a steel rod maintain a difference in their lengths of 10 c m at all temperatures. If their coefficients of expansion are 1.6 × 1 0 - 5 K - 1 ⁡ and 1.2 × 1 0 - 5 K - 1 ⁡ , then the length of the copper rod is, 40 c m, 30 c m, 32 c m, 24 c m

MARKS App · Accepted Answer

Δ l 1 = Δ l 2 ⇒ l 1 α 1 Δ T = l 2 α 2 Δ T ⇒ l 1 α 1 = l 2 α 2 ⇒ l 2 l 1 = α 1 α 2 ⇒ l 2 l 1 - 1 = α 1 α 2 - 1 l 2 - l 1 l 1 = α 1 - α 2 α 2 ⇒ l 1 = α 2 l 2 - l 1 α 1 - α 2 l 1 = 1.2 × 1 0 - 5 ( 10 ) ( 1.6 – 1.2 ) × 1 0 - 5 cm ⇒ l 1 = 30 c m

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