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A clock with an iron pendulum keeps correct time at 20⁰C . If the coefficient of linear expansion of iron is 0.000012 /⁰C and the room temperature is 30⁰C it loses in a day

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3.85s

2.67s

5.18s

1.38s

answer is D.

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Detailed Solution

time loss in 1 sec (1 oscillation):

$∆ T_{1} = \frac{1}{2} \frac{∆ l}{l} = \frac{1}{2} α (∆ θ)$

time loss in 1 day (1 day = 86400 sec):

$∆ T = \frac{1}{2} α (∆ θ) \times 86, 400 = \frac{1}{2} \times 12 \times 10^{- 6} \times 10 \times 86, 400 = 6 \times 10^{- 6} \times 864 \times 10^{3} = 5184 \times 10^{- 3} = 5.184 \sec$

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