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A pendulum clock with an iron rod keeps correct time at 20 deg C. If iron's linear expansion coefficient is 1.2 * 10⁻⁵ per deg C, by how much and in which sense will the clock be off after 24 hours at 40 deg C?

1. 10.4 s, fast
2. 10.4 s, slow
3. 20.8 s, fast
4. 20.8 s, slow

Correct answer: 10.4 s, slow

Solution

Heating lengthens the rod, increasing the period; the loss is (1/2)*alpha*delta_T*86400 ~= 10.4 s slow.

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