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Question

A seconds pendulum clock has a steel wire. The clock shows correct time at 25C. How much time does the clock lose or gain in one week, when the temperature is increased to 35C ? (αsteel=1.2×105/C)

A
5.18 s gain
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B
5.18 s lose
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C
36.28 s gain
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D
36.28 s lose
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Solution

The correct option is D 36.28 s lose
Time period T=2πlg
length changes as temperature increases

l35=l25(1+αΔθ)

T35=2πl35g

T25=2πl25g

So, T35=2πl25(1+αΔθ)g

T35=T25(1+αΔθ)12

for αΔθ<<1

T35=T25(1+12αΔθ)

T35=T25+I25×12αΔθ

T35T25=ΔT=T25×12αΔθ =7×24×60×60×0.5×1.2×105×10 =36.28 s

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