Question 1

How fast should a moving clock travel if it is to be observed by a stationary observer as running at one-half its normal rate?

Accepted Answer

The answer of How fast should a moving clock travel...

Question 2

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe
A) your watch slowing down.
B) your watch speeding up.
C) your watch losing time.
D) your watch gaining time.
E) nothing unusual about your watch.

Accepted Answer

According to the theory of relativity, time dilation affects observers in different frames of reference. As a passenger on the spaceship, you remain in the same frame of reference as your watch, so you would not notice any change in its ticking rate.

Question 3

The principle of equivalence states that
A) the laws of physics are the same in all inertial frames of reference.
B) the speed of light is the same in any frame of reference.
C) clocks that move relative to one another keep time at different rates.
D) the length of an object depends on its speed relative to a given observer.
E) all physical experiments conducted in a uniform gravitational field and in an accelerated frame of reference give identical results.

Accepted Answer

The principle of equivalence states that the effects of gravity are completely equivalent to the effects of acceleration. This means that any physical experiments conducted in a uniform gravitational field and in an accelerated frame of reference will give identical results, which is option E. Options A, B, C, and D are not relevant to the principle of equivalence.

Question 4

Which of the following results shows the validity of the relativistic effect of time dilation?
A) the detection of gravity waves
B) bending of light near the Sun
C) the decay of muons
D) red shift in distant galaxies
E) blue shift in distant galaxies

Accepted Answer

The decay of muons is a result of the time dilation effect predicted by relativity. Muons are a type of particle that are produced in Earth's atmosphere by cosmic rays. They have a very short lifetime of about 2.2 microseconds when measured at rest. However, because they travel at near the speed of light, time appears to slow down for them relative to an observer on Earth. This means that, from our perspective, muons appear to have a longer lifetime than they actually do, allowing them to travel further and be detected on the ground. This effect has been observed in experiments and is a direct confirmation of the time dilation effect predicted by relativity.

Question 5

Suppose one twin takes a ride in a space ship traveling at a very high speed to a distant star and back again, while the other twin remains on Earth. The twin that remained on Earth predicts that the astronaut twin is
A) younger.
B) the same age.
C) older.
D) cannot be determined from the given information

Accepted Answer

According to the theory of relativity, time dilation occurs as velocity increases. The closer an object's velocity is to the speed of light, the slower time will pass for that object relative to a stationary observer. Therefore, the twin traveling in the high-speed spaceship will experience time passing more slowly than the twin who stayed on Earth. As a result, when the traveling twin returns to Earth, they will have aged less than the twin who remained on Earth, making the twin on Earth older than the traveling twin.

Question 6

A 30-year-old astronaut goes off on a long term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, the astronaut's age would be
A) more than 50 years.
B) exactly 50 years.
C) less than 50 years.
D) exactly 30 years.
E) exactly 25 years.

Accepted Answer

According to the theory of relativity, time dilation occurs at high speeds close to that of light. This means that time passes more slowly for the astronaut relative to Earth. For a 20-year mission on Earth, the astronaut's biological age would be less than 50 years as measured by Earth because time dilation would cause them to age more slowly during the mission.

Question 7

Observer A sees a pendulum oscillating back and forth in a relativistic train and measures its period to be T_A. Observer B moves together with the train and measures the period of the pendulum to be T_B. These two results will be such that A) T_A > T_B. B) T_A = T_B. C) T_A < T_B. D) T_A could be greater or smaller than T_B depending on the direction of the motion.

Accepted Answer

Due to time dilation in special relativity, the period measured by Observer A, who is stationary relative to the moving train, will be longer than the period measured by Observer B, who is moving with the train.

Question 8

As the velocity of an inertial frame of reference increases with respect to a stationary observer, Einstein's theory of special relativity predicts that the length of an object, measured in the dimension parallel to the motion of the reference frame, will
A) decrease.
B) remain unchanged.
C) increase.
D) increase at first but start to decrease when the speed of the reference frame equals half the speed of light.
E) decrease at first but start to increase when the speed of the reference frame equals half the speed of light.

Accepted Answer

This is known as length contraction and is a consequence of time dilation in special relativity. As an object moves relative to an observer, its length in the direction of motion appears shorter to the observer. This effect becomes more significant as the velocity of the object approaches the speed of light.

Question 9

A spaceship visits Alpha Centauri and returns to Earth. Alpha Centauri is 4.5 light-years from Earth (our second closest star). The spaceship travels at one-half the speed of light for essentially all of its expedition.
(a) How long was the ship gone according to an observer on the Earth?
(b) How long was the ship gone according to an observer on the spaceship?

Accepted Answer

The answer of A spaceship visits Alpha Centauri and returns...

Question 10

Observer A sees a ruler moving by in a relativistic train and measures its length to be L_A. Observer B moves together with the train and measures the length of the ruler to be L_B. These two results will be such that A) L_A > L_B. B) L_A = L_B. C) L_A < L_B. D) L_A could be greater or smaller than L_B depending on the direction of the motion.

Accepted Answer

According to the theory of special relativity, length contraction occurs when an object moves relative to an observer. The length contraction factor is given by γ = 1/√(1- v^2/c^2), where v is the relative velocity between the observer and the object, and c is the speed of light. As observer A sees the ruler moving, the ruler appears shorter to observer A than to observer B who is moving with the ruler. Therefore, L_A < L_B.

Question 11

The special theory of relativity sets a limit on speed. Does it set a limit on momentum?
A) Yes
B) No

Accepted Answer

The special theory of relativity does not set a limit on momentum. As an object's speed approaches the speed of light, its relativistic mass increases, allowing its momentum to increase without bound.

Question 12

A spaceship traveling at constant speed passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?
A) the Earth frame of reference
B) the Mars frame of reference
C) the spaceship frame of reference
D) any inertial frame of reference
E) any frame of reference, inertial or not

Accepted Answer

According to the theory of relativity, the proper time is measured in the frame of reference of the observer who is at rest relative to the events being measured. In this case, the only observer who is at rest relative to both events is the spaceship. Therefore, the amount of time separating these two events is the proper time in the spaceship frame of reference.

Question 13

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe
A) your mass increasing.
B) your mass decreasing.
C) your mass varying erratically.
D) nothing unusual about your mass.

Accepted Answer

As the speed of the spaceship increases, the passenger's mass will not change. Mass is a fundamental property of an object and is not affected by its motion.

Question 14

FIGURE 29-1 
-An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The length of this object, as measured by a stationary observer,
A) approaches infinity.
B) approaches zero.
C) increases slightly.
D) decreases slightly.
E) does not change.

Accepted Answer

According to the theory of relativity, as an object approaches the speed of light, it experiences time dilation and length contraction. Therefore, as the object approaches the speed of light, its length, as measured by a stationary observer, approaches zero.

Question 15

FIGURE 29-1 
-An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The width of this object, as measured by a stationary observer,
A) approaches infinity.
B) approaches zero.
C) increases slightly.
D) decreases slightly.
E) does not change.

Accepted Answer

According to the theory of relativity, length contraction only occurs in the direction of motion. Since the width is perpendicular to the direction of motion, it remains unchanged for a stationary observer.

Question 16

The special theory of relativity sets a limit on speed. Does it set a limit on energy?
A) Yes
B) No

Accepted Answer

The special theory of relativity does not set a limit on energy. As an object's speed approaches the speed of light, its energy increases without bound, meaning energy can become infinitely large.

Question 17

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe
A) the length of your spaceship getting shorter.
B) the length of your spaceship getting longer.
C) the length of your spaceship varying erratically.
D) nothing unusual about the length of your spaceship.

Accepted Answer

According to the theory of relativity, length contraction occurs in the direction of motion relative to an outside observer, not to someone inside the spaceship. As a passenger, you would not notice any change in the length of your spaceship.

Question 18

A moving object's mass is twice its rest mass. Its length (in the direction of travel) must therefore be
A) one-half its proper length.
B) twice its proper length.
C) one-fourth its proper length.
D) four times its proper length.
E)  times its proper length.

Accepted Answer

The answer of A moving object's mass is twice its...

Question 19

FIGURE 29-1 
-An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in Figure 29-1. From the point of view of an observer who sees the spaceship moving to the right with a speed approaching c, the angle the bed makes with the floor
A) is greater than the angle observed by the astronaut.
B) is the same as the angle observed by the astronaut.
C) is smaller than the angle observed by the astronaut.
D) could be greater or smaller than the angle observed by the astronaut depending on the actual speed of the craft.

Accepted Answer

The angle is greater than the angle observed by the astronaut because the spaceship is moving to the right with a speed approaching c, which causes the bed to appear to be tilted more to the right from the observer's point of view.

Question 20

When a current flows through an inductor, its mass
A) decreases.
B) increases.
C) stays the same.
D) oscillates.

Accepted Answer

The mass of an inductor increases when a current flows through it due to the energy stored in the magnetic field, according to the principle of mass-energy equivalence (E=mc²).

Quiz 29: Relativity

How fast should a moving clock travel if it is to be observed by a stationary observer as running at one-half its normal rate?

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe

The principle of equivalence states that

Which of the following results shows the validity of the relativistic effect of time dilation?

Suppose one twin takes a ride in a space ship traveling at a very high speed to a distant star and back again, while the other twin remains on Earth. The twin that remained on Earth predicts that the astronaut twin is

A 30-year-old astronaut goes off on a long term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, the astronaut's age would be

Observer A sees a pendulum oscillating back and forth in a relativistic train and measures its period to be TA. Observer B moves together with the train and measures the period of the pendulum to be TB. These two results will be such that

As the velocity of an inertial frame of reference increases with respect to a stationary observer, Einstein's theory of special relativity predicts that the length of an object, measured in the dimension parallel to the motion of the reference frame, will

Observer A sees a ruler moving by in a relativistic train and measures its length to be LA. Observer B moves together with the train and measures the length of the ruler to be LB. These two results will be such that

The special theory of relativity sets a limit on speed. Does it set a limit on momentum?

A spaceship traveling at constant speed passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe

FIGURE 29-1 -An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The length of this object, as measured by a stationary observer,

FIGURE 29-1 -An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The width of this object, as measured by a stationary observer,

The special theory of relativity sets a limit on speed. Does it set a limit on energy?

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe

A moving object's mass is twice its rest mass. Its length (in the direction of travel) must therefore be

FIGURE 29-1 -An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in Figure 29-1. From the point of view of an observer who sees the spaceship moving to the right with a speed approaching c, the angle the bed makes with the floor

When a current flows through an inductor, its mass

Observer A sees a pendulum oscillating back and forth in a relativistic train and measures its period to be T_A. Observer B moves together with the train and measures the period of the pendulum to be T_B. These two results will be such that

Observer A sees a ruler moving by in a relativistic train and measures its length to be L_A. Observer B moves together with the train and measures the length of the ruler to be L_B. These two results will be such that