A clock with a metal pendulum beating seconds keeps correct time at `0^(@)C.` If it loses 12.5 s a day at `25^(@)C` the coefficient of linear expansion of metal pendulum is

Options

A. `(1)/(86400)/^(@)C`
B. `(1)/(43200)/^(@)C`
C. `(1)/(14400)/^(@)C`
D. `(1)/(28800)/^(@)C`

Answer

A

Explanation

Per second change `=(1)/(2)alphaDeltatheta`
So net lag in time `=((1)/(2)alphaDeltatheta)86400(1day=86400sec)or,12.5s=(1)/(2)(alphaDeltatheta)86400`
`(25)/(86400Deltatheta)=alphaor, alpha=(1)/(86400)/^(@)C`