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A clock with an iron pendulum keeps corr...

A clock with an iron pendulum keeps correct time at `20^(@)C`. How much time will it lose or gain in a day if the temperature changes to `40^(@)C`. Thermal coefficient of liner expansion `alpha = 0.000012 per^(@)C`.

A

10.3 second/day

B

20.6 second/day

C

5 second/day

D

20 minute/day

Text Solution

Verified by Experts

The correct Answer is:
A
(a)Time period `T prop sqrt(l)`
`implies(Delta T)/(T)=(1)/(2)(Deltal)/(l)=(1)/(2)alphaDeltatheta`
Also according to thermal expansion `l'=l(1+alphaDeltatheta)`
`(Deltal)/(l)=alphaDeltatheta.`
Hence , `(DeltaT)/(T)=(1)/(2)alphaDeltatheta`
`=(1)/(2)xx12xx10^(-6)xx(40-20)=12xx10^(-5)`
`implies DeltaT=12xx10^(-5)xx86400` second/day
`therefore Delta T~~10.3` second/day
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