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Question

A clock which keeps correct time at 25C has a pendulum made of brass whose coefficient of linear expansion is 0.000019. How many seconds a day will it gain if the temperature fall to 0C.

A
10.52 sec.
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B
20.52 sec.
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C
220.52 sec.
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D
202 sec.
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Solution

The correct option is B 20.52 sec.
Let L0 and L25 be the length of pendulum at 0C and 25C respectivelyWe know thatL25=L0(1+αT)=L0(1+0.000019×25)=1.000475 L0If T25 and T0 be the time periods at 25C and 0C respectively, thenT25=2π(L25g) and T0=2π(L0g)T25T0=(L25g)=(1.000475L0L0)=(1.000475)=1.000237Now T25T0T0=0.000237Gain in time for one vibration2×0.000237 secNumber of vibration in one day=24×60×602sec.(T=2 sec)Hence, the gain in time in one day=2×0.000237×24×60×602=20.52 sec

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