A pendulum clock lose 12 s a day if the temperature is 40°C and gains 4 s a day if the temperature is 20°C. The temperature at which the clock will show correct time, and the co-efficient of linear e…

Question

A pendulum clock lose 12 s a day if the temperature is 40°C and gains 4 s a day if the temperature is 20°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:

Accepted Answer

Correct answer: D. (d) 1 22 4×3 6 0 0= 12α (40 – T) ...(i) –42 4×3 6 0 0= 12 α (20 – T) ...(ii) from equation (i) and (ii) –3 = 4 0–T2 0–T – 60 + 3T = 40 – T 4T = 100 T = 25 from equation (ii) –42 4×3 6 0 0= 12 α (20 – 25) 42 4×3 6 0 0= 12 × α × 5 α = 82 4×3 6 0 0×5 = 1.85 × 10^–5/°C

$A pendulum clock lose 12 s a day if the temperature is 40°C and gains 4 s a day if the temperature is 20°C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively:$

Solution

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