A pendulum clock loses 12 s a day if the temperature is 40 o C and gains 4s a day if the temperature is 20 o…

A pendulum clock loses 12 s a day if the temperature is 40o C and gains 4s a day if the temperature is 20o C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion α of the metal of the pendulum shaft are respectively:
  1. 30oC;α=1.85×10-3 / oC
  2. 55oC;α=1.85×10-2 / oC
  3. 25oC;α=1.85×10-5 / oC
  4. 60oC;α=1.85×10-4 / oC

Solution

TT=12ll=12αθ 

124=40-θθ-20

3θ-60=40-θ

4θ=100

θ=25oC

Also,T=12α θ×T

4=12α 5×86400 

85×86400=α 

α=1.85×10-5  /oC  

Asked in: JEE Main 2016 (03 Apr)

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