The period of a simple pendulum is measured to be 4.0 seconds in a frame of reference. Which of the following is correct when the period of the pendulum is measured by an observer moving with half the speed of the light?

Choose one answer.
a. The time period of the pendulum remains constant.
b. The time period of the pendulum increases.
c. The time period of the pendulum decreases.
d. The time period of the pendulum decreases by half.

Answer = a.

To answer this question, we need to understand the concept of time dilation. Time dilation is a phenomenon in which the time experienced by an object or event depends on the relative velocity between the observer and the object or event being observed.

According to Einstein's theory of relativity, when an observer moves at high speeds relative to an object, time appears to slow down for the moving observer compared to a stationary observer.

In this scenario, the observer is moving with half the speed of light. Considering that this is a significant fraction of the speed of light, we can expect time dilation effects to be noticeable.

Since the period of a pendulum is the time it takes for one complete swing, if time is dilated, then the period will also be affected.

Based on the knowledge of time dilation, we can conclude that the correct answer is:

c. The time period of the pendulum decreases.

Therefore, as observed by an observer moving at half the speed of light, the period of the pendulum would appear to be shorter compared to the period measured in a stationary frame of reference.