A clock which has brass pendulum beats correctly at 30C will it run faster or slower if temperature increase or decrease

We know that the period of a pendulum is written as:

T = 2*pi*√(L/g)

where:

g = gravitational acceleration = 9.8m/s^2

pi = 3.1415...

L =  length of the pendulum, in this case, is the length of the brass pendulum.

Now, we know that the brass dilates when the temperature increases.

Then if the temperature increases, the value of L will increase, which means that the period T will also increase, because L is in the numerator of T.

If the period increases the complete motion of the pendulum needs more time, this would mean that the clock will run slower.

If the temperature decreases, the opposite occurs, the value of L decreases, and then the period also decreases, which means that the clock will run faster.

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