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Question

A pendulum clock having copper rod keeps correct time at 20C. It gains 15 seconds per day if cooled to 0C. Calculate the coefficient of linear expansion of copper.

A
1.7×105C1
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B
2.7×105C1
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C
3.7×105C1
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D
4.7×105C1
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Solution

The correct option is A 1.7×105C1
Time period at any temperature T is
tT=2πlTg;t0=2πl0gtTt0=lTl0=l0[1+α(ΔT)]l0tTt01+αT1+ααTtTt01=α2TtTt0t0=αTαt20t0t0=αTα=α×10C
Time gained in 24 hours, ΔT=24 hrs×(α.10)
15s=24×60×60×α×10α=1.7×105C1

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