A clock with a metallic pendulum gains `5 s` each day at a temperature of `15^@C` and loses `10 s` each day at a temperature of `30^@C`. Find the coefficient of thermal expansion of the pendulum metal.

Options

A. `83xx10^-6K^-1`
B. `28xx10^-6K^-1`
C. `23xx10^-6K^-1`
D. `43xx10^-6K^-1`

Answer

C

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`