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 of pendulum is

Explanation

`T=2pisqrt((l)/(g))`
`2xx(86400)/(86400+5)=2pisqrt((l_(15))/(g))`
and `2xx(86400)/(86400-10)=2sqrt((l_(30))/(g))`
dividing `sqrt((l_(30))/(l_(15)))=(86405)/(86390)`
or `sqrt((l_(15)(1+alphaxx15))/(l_(15)))=1+(15)/(86390)`
or `(1+15alpha)^((1)/(2))=1+(15)/(86390)`
or `1+(1)/(2)xx15alpha=1+(15)/(86390)`
or `alpha=23xx10^-6K^-1`