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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 = `1/2propDeltatxx86,400s`
At `15^(@)C` clock is 5s fast. At `30^(@)C` it is 10s slow.
Between `15^(@)C` & `30^(@)C` at temperature `t^(@)C` it will show correct time.
`DeltaTpropDeltatrArr5/10=((t-15))/((30-T))rArrt=20^(@)C`
Loss of time per day = `1/2propDeltatxx86,400`
`10=1/2xxpropxx(30-20)xx86,400`
`rArrprop=2.31xx10^(-5)//""^(@)C`
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