# How does thermal expansion affect the accuracy of a pendulum clock?

##### 1 Answer

**the clock will become slower by a small amount due to expansion**

#### Explanation:

A pendulum clock has the Time Period

By thermal expansion the length of the pendulum will increase say by a small amount

so the new time period

so,

or

so the time period of oscillation will increase , thereby the clock will give time as if slow by **(T'-T)**

In clocks people use seconds pendulum whose time period os 2 secs and length is about 1m and if the length increases to say 1.001 m

then T'- T = 2 s . {sqrt ( 1.001)- 1 }

so the error can be estimated.