Properties Of Solids And Liquids Question 412
Question: A pendulum clock loses 12 s a day if the temperature is $ 40{}^\circ C $ and gains 4 s a day if the temperature is$ 20{}^\circ C $ . The temperature at which the clock will show correct time, and the co- efficient of linear expansion $ (\alpha ) $ of the metal of the pendulum shaft are respectively:
Options:
A) $ 30{}^\circ C;\alpha =1.85\times {{10}^{-3}}/{}^\circ C $
B) $ 55{}^\circ C;\alpha =1.85\times {{10}^{-2}}/{}^\circ C $
C) $ 25{}^\circ C;\alpha =1.85\times {{10}^{-5}}/{}^\circ C $
D) $ 60{}^\circ C;\alpha =1.85\times {{10}^{-4}}/{}^\circ C $
Show Answer
Answer:
Correct Answer: C
Solution:
Time lost / gained per day $ =\frac{1}{2}\alpha \Delta \theta \times 86400 $
second $ 12=-\alpha ( 40-8 )\times 86400 $ ….(i) $ 4=-\alpha ( \theta -20 )\times 86400 $ ….(ii) On dividing we get, $ 3=\frac{40-\theta }{\theta -20} $
$ 36-60=40-\theta $
$ 4\theta =100\Rightarrow \theta =25{}^\circ C $
