A clock pendulum made of aluminum has a period of 030 s and

A clock pendulum, made of aluminum, has a period of 0.30 s and is accurate at 12.0oC. If the clock is used in a climate where the temperature averages 27.0oC what correction is necessary at the end of a 24 day period to the time given by the clock? Answer is not 88.6s

Solution

Here ,

Ti = 0.30 s

let the initial length is Lo

Now , at 27 degree C

L = Lo * (1 + alpha * del T)

L = Lo * (1 + 22.2 *10^-6 * (27 - 12))

L = 1.000333 Lo

Now , for the time period

as Tf/Ti = sqrt(L/Lo)

Tf/.30 = sqrt(1.000333)

Tf = 0.3000499 s

Now , for a period of 24 hour

correction needed = 0.3000499/0.30 * (3600 * 24) - 3600 * 24

correction needed = 14.38 s

the correction necessary at the end is 14.38 s