Chapter 26, Problem 1CQ

Choose the option from each pair that makes the following statement correct. According to an observer at rest, moving clocks run more [(a) slowly; (b) quickly] than stationary clocks and moving rods are [ (c) longer; (d) shorter] than stationary rods.

To determine

The time measured by moving clocks versus the time measured by the stationary clock.

Answer to Problem 1CQ

According to an observer at rest, moving clocks run more (b) quickly than the stationary clocks.

According to an observer at rest, moving rods are (d) shorter than stationary rods.

Explanation of Solution

Time dilation: According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field.

Length contraction: Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length which is the length as measured in the object’s own rest frame.

Conclusion:

The time measured by the observer at the rest frame with the stationary clocks is the proper time. The proper time measured by the stationary clocks will be slower than the time measure in the moving clocks. Thus, the choice (b) is correct.

The time measured by the moving clocks will be shorter than the time measured by the stationary clocks according to the time dilation. Thus, the choice (a) is incorrect.

The length of the rod measured when it is at rest is its proper length. When the rod is moving with a speed near to the speed of light, the length will appear shorter according to the length contraction. Thus, the choice (d) is correct.

The length of a stationary rod measures according to the rest frame is longer compared to the moving rod with respect to the rest frame.  Thus, the choice (c) is incorrect