A clock which keeps correct time at 25∘C 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 0∘C.
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. LetL0andL25bethelengthofpendulumat0∘Cand25∘CrespectivelyWeknowthatL25=L0(1+αT)=L0(1+0.000019×25)=1.000475L0IfT25andT0bethetimeperiodsat25∘Cand0∘Crespectively,thenT25=2π√(L25g)andT0=2π√(L0g)∴T25T0=√(L25g)=√(1.000475L0L0)=√(1.000475)=1.000237NowT25−T0T0=0.000237∴Gainintimeforonevibration2×0.000237secNumberofvibrationinoneday=24×60×602sec.(∵T=2sec)Hence,thegainintimeinoneday=2×0.000237×24×60×602=20.52sec