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Question

A pendulum clock gives correct time at 20 C at a place where g = 9.800 ms2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g 9.788 ms2. At what temperature will it give correct time ? Coefficient of linear expansion of steel =12×106 C1

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Solution

g1=9.8 m/s2,

g2=9.788 m/s2

T1=2πl1g1

T2=2πl2g2

=2πl2(1+αT)g2

αsteel=12×106/C

Q1=20

Q2=?

T1=T2

2πl1g1=2πl1(1+αΔT)g2

(l1g1)=l1(1+αΔT)g2

19.8=1+12×106×ΔT9.788

9.7889.8=1+12×106×ΔT

9.7889.81=12×106×ΔT

ΔT=0.0012212×106

T220=102.4

T2=102.4+20

=82.482C


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