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JEE Main 20163 April
Exam
JEE Main
Year
2016
Date
3 April
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2016 · 3 April · Physics · Thermal Properties of Matter

A pendulum clock loses 12 s a day if the temperature is 40 ^ o C...

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:

Options

  1. A30oC;α=1.85×10−3{30}^{o}C; \alpha = 1.85 \times {10}^{- 3} / oCoC
  2. B55oC;α=1.85×10−2{55}^{o}C; \alpha = 1.85 \times {10}^{- 2} / oCoC
  3. C25oC;α=1.85×10−5{25}^{o}C; \alpha = 1.85 \times {10}^{- 5} / oC{}^{o}C
  4. D60oC;α=1.85×10−4{60}^{o}C; \alpha = 1.85 \times {10}^{- 4} / oCoC

Correct answer

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

Step-by-step solution

∆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 = \dfrac{1}{2}\alpha ∆ \theta \times T<br/><br/><br /><br />4 = \dfrac{1}{2}\alpha5 \times 86400<br/><br/><br /><br />\dfrac{8}{5 \times 86400} = \alpha<br/><br/><br /><br />\alpha = 1.85 \times {10}^{- 5} {/}^{o}C
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