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Question

A pendulum clock gives correct time at 20C at a place where g=9.800 m s2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g=9.788 m s2. At what temperature will it give correct time? Coefficient of linear expansion of steel =12×106C1.

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Solution

Given that g=9.8m/s2 and g=0.012m/s2

Time period of pendulum is given by :
T=2πLg

We get,
TT=12(LLgg)(L)

using linear expansion of steel rod,
LL=αT (T:change in temperature)

So, maintain its time (i.e.T=0) we get-
LL=gg

αT=gg

(T20)=0.0129.8×12×106

T20 102.0482.040c

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