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

No. of seconds lost in a day-
`Delta t = (1)/(2) alpha Delta theta xx 86400`
`rArr alpha = (2 Delta t)/(Delta theta xx 86400) = (2 xx 12.5)/(25 xx 86400)`
`rArr alpha = (1)/(86400) // ""^(@)C`.