Given:
Coefficient of linear expansion: α = 2.4 × 10^–5 °C^–1.
Temperature change in winter: Δ T₁= 5° C
Temperature change in summer : Δ T₂ = 45° C
Formula Used:
For torsional pendulum, the time period is given as:
Here, I is the moment of inertia of the wire and k is the torque constant of the wire.
Due to change in temperature the moment of inertia will also change.Hence,
Here, I’ is the changed moment of inertia and I₀ is the initial moment of inertia at 0 ° C
During winters:Substituting for time period in winter: t₁



During Summers :
Substituting for time period in summer: t₂


Hence we know time period of torsional pendulum in winter and summer.
Percentage change is given as:

Here, the numerator is the change in time period and the denominator is the original time period.




Hence the percentage change in the time period between peak winter (5°C) and peak summer (45°C) is 0.0959%