A pendulum clock gives correct time at 20 degree Celsius at a place where g= 9.800 m/s^2. 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/s^2. At what temperature will it give correct time?coefficient of linear expansion of steel = 12x 10^-6/ degree celsius.

Dear Cathy,

Ans: The time period is T=2∏√(L/g)

So if the time period is the same then we get,

T=constant hence L1/L2=g1/g2

Now as the value of g is decreasing and hence temp must be decreased to get the same value of T. Now L2=L1(1-αt)

solving we get,

t= -122 degree

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