Question

A pendulum clock shows correct time at ${{0}^{\circ }}C$. At a higher temperature the clock
A. loses time.
B. gains time.
C. neither lost nor gained time.
D. will not operate.

Answer 1

The time period of oscillations of a simple pendulum is given as $T=2\pi \sqrt{\dfrac{l}{g}}$, where l is the length of the string and g is acceleration due to gravity. When the temperature rises, the string will expand. Use the formula for time period and figure what happens when the length is increased.

Formula used:
$T=2\pi \sqrt{\dfrac{l}{g}}$

Complete answer:
A pendulum clock is a clock in which the time is measured with reference to the oscillations of a pendulum.
Suppose a pendulum, whose string is of length l is hanging from a ceiling. Let the pendulum undergo a simple harmonic motion. Since it is a periodic motion, the pendulum will have a time period of motion.
The time period of motion of the pendulum is given as $T=2\pi \sqrt{\dfrac{l}{g}}$ ….. (i),
where g is the acceleration due to gravity.
Now, if they raise the temperature, the string of the pendulum will expand. As a result, the length of the string will increase.
According to equation (i), if length l will increase, the value of T will also increase.
This means that when the temperature is increased, the time period of oscillation of the pendulum increases.
If the time period increases, then the pendulum will complete less than the required oscillation for a given time interval.
Hence, we say that at higher temperature, the pendulum loses time.

This means that the correct option is A.

Note:
We now know that with change in temperature, the time period of a pendulum changes.
The time period of a pendulum also depends on the altitude where it undergoes oscillations. This is because the value of g i.e. acceleration due to gravity changes with the altitude.