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A clock with a metallic pendulum is 5 se...

A clock with a metallic pendulum is 5 seconds fast each day at a temperature of `15^(@)C` and 10 seconds slow each day at a temperature of `30^(@)C`. Find coefficient of linear expansion for the metal.

Text Solution

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Loss (or) gain of time per day `= (1)/(2) prop Delta t xx 86 , 400 ` s
At `15^(0)C` clock is 5s fast. At ` 30^(0)C ` it is 10s slow.
Between `15^(0)`C & `30^(0)`C at temperature `t^(0)C` it will show correct time.
`Delta T prop Delta rArr (5)/(10) = ((t - 15))/((30 - T)) rArr t = 20^(0)C `
Loss of time per day = `(1)/(2) prop Delta t xx 86 , 400`
10 `= (1)/(2) xx prop xx (30 - 20) xx 86, 400`
`rArr prop = 2.31 xx 10^(-5) //^(0)` C
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