A clock with a metallic pendulum is 5 seconds fast each day at a temperature of 15^(0)C and 10 seconds slow each day at a temperature of 30^(0)C. Find coefficient of linear expansion Jor the metal.

A clock with a metallic pendulum is 5 seconds fast each day at a tempe

1.	A clock with a metallic pendulum is 5 seconds fast each day at a temperature of 15^(0)C and 10 seconds slow each day at a temperature of 30^(0)C. Find coefficient of linear expansion Jor the metal.
Answer» Solution :Loss (or) gain of time per day `= (1)/(2) prop Delta t xx 86 , 400 ` s At `15^(0)C` clock is 5s fast. At ` 30^(0)C ` it is 10S slow. Between `15^(0)`C & `30^(0)`C at temperature `t^(0)C` it will show correct time. `Delta T prop Delta rArr (5)/(10) = ((t - 15))/((30 - T)) rArr t = 20^(0)C ` Loss of time per day = `(1)/(2) prop Delta t xx 86 , 400` 10 `= (1)/(2) xx prop xx (30 - 20) xx 86, 400` `rArr prop = 2.31 xx 10^(-5) //^(0)` C