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A pendulum clock, made of a material having coefficient of linear expansion `alpha=9xx10^(-7)//.^(@)C` has a period of 0.500 sec at `20^(@)C`. If the clock is used in a climate where temperature averages `30^(@)C`, what correction is necessary at the end of 30 days to the time given by clock?A. `2.5xx10^(-7)` sB. `5xx10^(-7)s`C. `1.125xx10^(-6)s`D. `2.25xx10^(-6)` s |
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Answer» Correct Answer - D Given, the coefficient of linear expansion, `alpha=9xx10^(-7)""^(@)C^(-1)` Initial time period, `T_(0)=0.5 s`, initial temperature `T_(i) = 20°` C and final temperature, `T_(f) = 30°C` Expansion in length, `Deltal = l alpha (T_(f) - T_(i))` `!Deltal=lxx9xx10^(-7)(30-20)` Now, the time period of pendulum, `T=2pisqrt(l/g)` Error in time period, `(Deltat)/(T)=1/2(Deltal)/l+1/2(Deltag)/g` Since, `Deltag=0` `!(DeltaT)/T=1/2(Deltal)/l` Now, substituting values in the above equation we get, `!(Delta_(T))/(0.5)=1/2[(lxx9xx10^(-7))/l(30-20)]` `!DeltaT=(0.5xx9xx10^(-7)xx10)/2` `!DeltaT=2.25xx10^(-6)s` |
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