Question

What effect would the temperature have on the time kept by a pendulum clock if the pendulum rod increase in length with an increase in temperature

Answer 1

As we know the time period of pendulum is given by the equation

$T = 2\pi \sqrt{\frac{L}{g}}$

so here

L = length of the pendulum

Now on increasing the temperature due to thermal expansion the length of the pendulum will increase and due to this the time period of the pendulum will also increase

Now due to increase in time period of the pendulum the clock will become slow and it will give incorrect time due to this increase in temperature

Answer 2

Thermal expansion increases the pendulum period, and the clock will lose time

Further explanation

Simple Harmonic Motion is the motion of an object (repetitive movement) through its equilibrium point where the frequency of vibrations / oscillation per second is constant

The motion that occurs in the pendulum is one example of simple harmonic motion

Terms used:

• Deviation (y): the object's distance from the balance point
• Amplitude (A): maximum deviation
• frequency (f): number of vibrations at any time
• Period (T): the amount of time in one vibration

Whereas the relationship T and f:

$\displaystyle T=\frac{1}{f}\\\\f=\frac{n}{t}$

n = number of vibrations / oscillation

t = time (s)

Formula used:

$\large{\boxed{\bold{T=2\pi \sqrt{\frac{L}{g} }}}\rightarrow \frac{1}{f}=2\pi \sqrt{\frac{L}{g} }$

From this formula shows that the period is proportional to the length of the pendulum rod . The longer the pendulum rod , the greater the amount of time in one vibration

If thermal expansion occurs in the pendulum clocks, the pendulum rod changes in length ,proportional to the temperature change, and increases the pendulum period, so the clock will lose time

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