Question

Which of the following has the time period two seconds specifically:
A) Wristwatch
B) Linear expansion of the iron rod
C) Frequency of ripples on the surface of the water
D) Seconds pendulum

Answer 1

Hint: Periodic motions are motions that are repeated at regular intervals of time. The time period of oscillation is defined as the time taken to complete one oscillation. A pendulum is one of the best examples of periodic motion. The time period of various types of pendulums depends on different factors.

Complete step by step solution:
Periods of oscillation are associated with periodic motions. Periodic motions can be rotatory, oscillatory, and vibratory in nature. The period of different systems depends on various factors. Let us consider one of the typical examples of periodic motion that is the simple pendulum.

A simple pendulum consists of a mass suspended by an inextensible massless string having a length. The other end of the length is fixed to a rigid support. When the mass is pulled to one side and released, the pendulum starts to execute to and fro oscillations. The time period of a simple pendulum depends on the length of the pendulum and gravity. The time period is independent of the mass attached to the pendulum.

We can adjust the length of the pendulum in such a way that the time taken for the completion of one oscillation is two seconds. Such a pendulum with a period of two seconds is called the second's pendulum.

The answer is Option (D): Second’s pendulum.

Note: We know that the time is taken by the wristwatch to complete one full rotation in 60 seconds. The frequency of ripples on the surface of the water is not known to have a fixed frequency. The frequency of ripples can change with various factors. The linear expansion of the iron rod is also not fixed. If the conditions change the rate of expansion also changes. Out of the four options, only the second’s pendulum has a fixed time period of two seconds.