Thermal Properties of Matter

JEE Main level, single correct, medium

43 of 126

Question 43 of 126

A simple pendulum made of a bob of mass m and a metallic wire of a negligible mass has a time period of 2s2s at T=0∘CT=0^{\circ}C. If the temperature of the wire is increased, and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope SS. If the coefficient of linear expansion of metal is α\alpha, then the value of SS is

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Answer: (C) α\alpha

△TT=12△ll=12α∆θ\dfrac{△T}{T}=\dfrac{1}{2}\dfrac{△l}{l}=\dfrac{1}{2}\alpha ∆\text{θ}
⇒∆T=12Tα∆θ\Rightarrow ∆T=\dfrac{1}{2}T\alpha ∆\text{θ}
∆T∆θ=T2α\dfrac{∆T}{∆\text{θ}}=\dfrac{T}{2}\alpha
But,
T=2sT=2s
∆T∆θ=α\dfrac{∆T}{∆\text{θ}}=\alpha

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