A pendulum clock having copper rod keeps correct time at 20∘C. It gains 15 seconds per day if cooled to 0∘C. Calculate the coefficient of linear expansion of copper.
A
1.7×10−5∘C−1
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B
2.7×10−5∘C−1
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C
3.7×10−5∘C−1
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D
4.7×10−5∘C−1
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Solution
The correct option is A1.7×10−5∘C−1 Time period at any temperature T is tT=2π√lTg;t0=2π√l0gtTt0=√lTl0=√l0[1+α(ΔT)]l0⇒tTt0√1+αT≈1+ααTtTt0−1=α2T⇒tT−t0t0=αTα⇒t20−t0t0=αTα=α×10∘C Time gained in 24 hours, ΔT=24hrs×(α.10) ⇒15s=24×60×60×α×10⇒α=1.7×10−5∘C−1