Question

An aluminium scale (a = 2.4 x 10-5 (Cº)-]
calibrated at 25°C is measuring length of copper rod
[a. = 1.7 x 10-5 (Cº)-] at 125°C. If the reading
shown is 100 m, then the correct reading is
(1) 100.7 m
(2) 100.07 m
(3) 107 m
(4) 170 m​

Answer 1

answer : option (2) 100.07 m

coefficient of linear expansion of copper, α = 1.7 × 10^-5/°C

coefficient of linear expansion of aluminium, α' = 2.4 × 10^-5/°C

temperature difference, ∆T = (125°C - 25°C) = 100°C

using , L_app = L_al - L_cu

= l(1 + α'∆T) - l(1 + α∆T)

= l(α' - α)∆T

= 100 × (2.4 - 1.7) × 10^-5 × 100

= 10⁴ × 0.7 × 10^-5

= 0.07 m

hence, correct reading is l + L_app = (100 + 0.07)m = 100.07m

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Answer 2

$\huge\bold\purple{Answer:-}$

(2) 100.07 m