Question

A pendulum clock loses 12 s a day if the temperature is 40 ° C and goes fast by 4s a day if the temperature is 20 ° C . find the temperature at which the clock will show correct time and the coefficient of linear expansion of the metal of the pendulum shaft .

Answer 1

Hello paridhi : - ) 

Let T be the temperature at which the clock is correct time lost per day = > α (

rise in temperature ) ×86400

12 = > 1α/2    (40-T)×86400 -------------------------------------------------   1 

Time gained per day => 1α/2 ( drop in temperature)×86400

4 = > 1α/2  ( T-20)×86400

Adding eqs 1 and 2 we get 

32 = > 86400 α (40-20) = > α=> 1.85 ×10^-5 l ° C

dividing eq 1 by 2 we get 

12 (T-20) = > 4(40-T) => T = > 25 ° C

Clock shows correct time at 25 °C 

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