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Coefficient of linear expansion of the wire, α = 2.4 × 10–5 °C–1Let I0 be the moment of inertia of the torsional pendulum at 0 °C.If K is the torsional constant of the wire, then time period of torsional pendulum
T:
T=2πIK …1Here, I = moment of inertia after change in temperatureWhen the temperature is changed by
∆θ, moment of inertia
I,I = I0(1+2
α ∆θ)On substituting the value of I in equation(1), we get:
T=2πI01+2α∆θKIn winter,
∆θ= 5 °C
∴Time period
T1
=2πI01+2α×5KIn summer,
∆θ= 45 °CTime period
T2
=2πI01+2α×45K
So,T2T1=1+90α1+10α =1+90×2.4×10-51+10×2.4×10-5⇒T2T1=1.002161.00024%change =T2T1-1×100 =0.0959%⇒%change in time period≈9.6×10-2%Therefore, the percentage change in time period of a torsional pendulum between peak winters and peak summers is 9.6 × 10–2 % .
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