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Question

A pendulum clock loses 12 s a day if the temperature is 40oC and gains 4 s a day if the temperature is 20oC. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively

A
25oC; α=1.85×105/oC
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B
60oC ; α=1.85×104/oC
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C
30oC; α=1.85×103/oC
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D
55oC; α=1.85×102/oC
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Solution

The correct option is A 25oC; α=1.85×105/oC
The time period of a pendulum is given by,
t=2πlg
Δt=2πgΔl2l
Δl=αΔθ
Δt=πglαΔT
Δt1Δt2=ΔT1ΔT2

124=40TT20
3T60=40T
T=25C

From Δt = πglαΔT,
α = 1.85×105/°C

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