Question

# A pendulum clock keeps correct time at 0∘C. Its mean coefficient of linear expansions is α/∘C, then the loss, in seconds, per day by the clock if the temperature rises by t∘C is -

A

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B

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C

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D

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Solution

## The correct option is B The gain/loss of time will be (T′−T) seconds. For example, what the clock was measuring to be 1 second will now be shown as 1(1+12aΔθ) seconds. Which is, to say, a gain of [1(1+12aΔθ)−1] seconds, or, 12aΔθseconds, has occurred. Thus, for T seconds,the clock will show a gain of T × 12aΔ θ seconds. T′ = T(1+12aΔθ) ⇒ T′ = T + 12aTΔθ Now, a day has 24 × 60 × 60 seconds = 86,400 seconds. You might have figured the answer now. Since, we are taking the measure at a temoerature θfinal = t∘C, and the clock is known to give a correct reading at θinitial = 0∘C, Δθ = t∘C. Also, T = 86,400 seconds.

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