Thermal Properties of Matter

JEE Main level, single correct, medium

44 of 126

Question 44 of 126

A pendulum clock loses 12 s a day if the temperature is 40o{40}^{o} C and gains 4s a day if the temperature is 20o{20}^{o} C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α)\left(\alpha \right) of the metal of the pendulum shaft are respectively:

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Answer: (C) 25oC;α=1.85×10−5{25}^{o}C;\alpha =1.85\times {10}^{-5} / oC{}^{o}C

∆TT=12∆ll=12α∆θ\dfrac{∆T}{T}=\dfrac{1}{2}\dfrac{∆l}{l}=\dfrac{1}{2}\alpha ∆\theta

124=40−θθ−20\dfrac{12}{4}=\dfrac{40-\theta }{\theta -20}

3θ−60=40−θ3\theta -60=40-\theta

4θ=1004\theta =100

θ=25oC\theta ={25}^{o}C

Also,∆T=12α∆θ×TAlso, ∆T=\dfrac{1}{2}\alpha ∆\theta \times T

4=12α5×864004=\dfrac{1}{2}\alpha 5\times 86400

85×86400=α\dfrac{8}{5\times 86400}=\alpha

α=1.85×10−5\alpha =1.85\times {10}^{-5} /oC{/}^{o}C

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