Question
A pendulum clock keeps correct time at 20^{o}C. The coefficient of linear expansion of pendulum is . If the room temperature increases to 40^{o}C, how many seconds will the clock lose or gain per day?

10.37 s

20.6 s

5 s

50 minutes
medium
Solution
10.37 s
The time period of a pendulum clock is given by
…(i)
Partially differentiating we get
Dividing (ii) by (i) we have
Where α is the coefficient of linear expansion and âˆ†θ is the rise in temperature. Thus
Now, the time period of a pendulum clock T = 1s. Thus the clock gains 12 × 10^{–5} s every second. In a day (= 86400 s), the clock will gain 12 × 10^{–5}× 86400 = 10.37 s.
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