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Question

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


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 C

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Let T be the temperature at which the clock is correct.

Time lost per day =

12 × a × (rise in temperature) × 86400 s, (see hint)

12 = 12 × a × (40T) × 86400. ...........(1)

Time gained per day -

12 × a × (rise in temperature) × 86400 s,

4 = 12 × a × (T20) × 86400. ...........(2)

On adding (1) and (2), we get

64 = 86400 × a × (4020)

a = 1.85 × 105/C.

On dividing (1) and (2), we get

12(T20) = 4(40T)

T = 25C

clock shows correct time at 25C only!


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