A clock with a metallic pendulum gains 6 seconds each day when the temperature is 20oC and loses 6 s

Question

A clock with a metallic pendulum gains 6 seconds each day when the temperature is 20oC and loses 6 second when the temperature is 40oC. Find the cofficient of linear expanion metal.

Accepted Answer

For simple clock gives correct time at temperature
⇒ T ∝ l^1/2 ⇒ αᐃθ
Assuming clock gives correct time at temperature
θ₀ ⇒ α(θ₀ - 20) &
α(40 - θ₀) ⇒ θ₀) = 30^oC
⇒ α = 1.4 × 10^-5 ^oC^-1

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