First slide

Thermal expansion

Question

A pendulum clock gives correct time at 20⁰C at a place where g= 10m/s². The pendulum consists of a light steel rod connected to a heavy ball. If it is taken to a different place where g = 10.01m/s² at what temperature the pendulum gives correct time (α of steel is 10^–5/⁰C)

Moderate

A

30⁰C
B

60⁰C
C

100⁰C
D

120⁰C

Solution

$\large T=2\pi \sqrt{\frac lg}$ Here T is constant, lαg
$\large \frac {\Delta l}{l}=\frac {\Delta g}{g}\Rightarrow \alpha(t_2-t_1)=\frac {\Delta g}{g}$
$\large 10^{-5}(t_2-20)=\frac {0.01}{10}\Rightarrow t_2=120^0C$

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