Question

What is the time period of a pendulum clock?

Answer 1

Hint: Let us first understand what a pendulum clock is? A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. It swings back and forth in a precise time interval. Pendulum clocks must be stationary to operate. Any motion or accelerations will affect the motion of the pendulum, causing inaccuracies.

Complete step by step solution:
The time taken to complete one oscillation is known as the time period of the pendulum. The pendulum swings with a period that varies with the square root of its effective length.
$$T=2\pi \sqrt{{\displaystyle \frac{L}{g}}}$$
where L is the length of the pendulum and g is the local acceleration of gravity.

While calculating the expression for the time period for a simple pendulum, we assume that there is negligible friction from the air, and gravity remains constant.
So basically the time period is the time taken to cover one oscillation. A pendulum clock takes 1 s to move from one extreme to the other extreme, so its time period is 2 s.

Note:
The vertical distance between the point of suspension and the centre of mass of the suspended body (when it is in the mean position) is called the length (L) of the simple pendulum. The vertical line passing through the fixed support is the mean position of a simple pendulum. If the temperature of a system changes then the time period of the simple pendulum changes due to a change in length of the pendulum.