A clock with a metallic pendulum is 5 sec fast each day at a temperature of 15^(2)C and 10 sec slow each day at a temperature of 30^(@)C. Find coefficient of linear expansion for the metal.

A clock with a metallic pendulum is 5 sec fast each day at a temperatu

1.	A clock with a metallic pendulum is 5 sec fast each day at a temperature of 15^(2)C and 10 sec slow each day at a temperature of 30^(@)C. Find coefficient of linear expansion for the metal.
Answer» Solution :Time LOST or gained per second by a pendulum clock is given by `deltat=(1)/(2)alpha DeltaT` Here if temperature is HIGHER than graduation temperature the clock will loose time and if it is lower than graduation temperature clock will GAIN time. Thus time lost or gained per day is `deltat=(1)/(2) alpha DeltaT xx 86400 ""`[as 1 day = 86400 s.] If graduation temperature of clock is `T_(0)` then we have , At `15^(@)C`, clock is gaining time, thus `5=(1)/(2).alpha.(T_(0)-15)xx86400 ""....(a)`, At `30^(@)C` clock is loosing time thus `10=(1)/(2) alpha (30-T_(0))xx86400""....(b)` Dividing EQUATION (b) by (a), we get 2 `(T_(0)-15)=(30-T_(0)) or T_(0)=20^(@)C` Thus from equation (a) `5=(1)/(2) xx alpha xx [20-15] xx86400 rArr alpha=(2.31xx10^(5)""^(@)C^(-1))`