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A pendulum clock keeps correct time at 0...

A pendulum clock keeps correct time at `0^(@)C`. Its mean coefficient of linear expansions is `alpha//.^(@)C`, then the loss in seconds per day by the clock if the temperature rises by `t^(@)C` is

A

`((1)/(2)alpha txx864000)/(1-(at)/(2))`

B

`(1)/(2)alpha txx86400`

C

`((1)/(2)alpha txx86400)/((1-(at)/(2))^(2))`

D

`((1)/(2)alpha txx86400)/(1+(alpha t)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
Loss in time per second,
`(DeltaT)/(T)=(1)/(2) alpha Delta theta=(1)/(2) alpha (t- 0)`
`rArr` loss in time per day,
`Deltat=(1)/(2) alpha t=(1)/(2) alpha t xx (24xx60xx60)=(1)/(2) alpha xx86400`
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