Question

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

Answer 1

Hint: A pendulum oscillates periodically about its mean position. The time interval after which it repeats its motion is known as its time period. When the temperature increases, the length of the pendulum also increases. The time period of the pendulum depends on the length of the pendulum and the acceleration due to gravity.

Complete answer:
A pendulum clock undergoes oscillation under the effect of the gravitational force.
The time period of the pendulum is given by-
$T=2\pi \sqrt{\dfrac{l}{g}}$
Here, $T$ is the time period of the pendulum
$l$ is the length of the pendulum
$g$ is the acceleration due to gravity
When the temperature of the surroundings increase, the thread holding the bob of the pendulum undergoes expansion, hence it is called thermal expansion. Le the new length be $l'$ and the new time period be $T'$. The value of new time period will be-
$T'=2\pi \sqrt{\dfrac{l'}{g}}$
 According to the above equation, as the length increases, the time period also increases so the pendulum is said to lose time. The time recorded by the pendulum will be more than the original time.
Therefore, the thermal expansion will increase the time period of the pendulum and hence make it less accurate.

Note:
The restoring force developed in the pendulum is due to gravity. It oscillates between two extreme positions and one mean position. The motion of the pendulum follows periodic motion and it repeats its motion after a time interval equal to its time period. It also follows simple harmonic motion.