Question 1

What happens to the density of an object as it moves with respect to an observer as compared to the same object at rest with respect to the same observer?
A) The density will decrease.
B) The density will remain unchanged.
C) The density will increase.
D) The density can either increase or decrease depending on its direction of motion with respect to the observer.

Accepted Answer

According to the theory of relativity, as an object moves relative to an observer, its length contracts in the direction of motion (length contraction), while its mass increases (relativistic mass increase). This results in an increase in density, as density is mass per unit volume.

Question 2

Fred and Joanne both measure the length of a particular spaceship to be 100 m when it is on Earth. Joanne then gets into the spaceship and, after visiting the Moon, hurtles past Earth at a speed close to the speed of light. Fred, still on Earth, measures the length of the moving spaceship to be about 90 m. At the same time, Joanne (using her own meterstick) measures the length of the spaceship to be
A) about 90 m because of the motion of the spaceship.
B) 100 m because she is "at rest" on the spaceship.
C) It cannot be concluded from the information given.
D) about 110 m because both she and the spaceship are moving.

Accepted Answer

Joanne is in the same inertial frame as the spaceship, so from her perspective, the spaceship is not undergoing length contraction. Length contraction is observed by an observer in a different inertial frame, such as Fred's, who sees the spaceship moving at a significant fraction of the speed of light.

Question 3

Suppose an observer sees a spaceship with a clock on it hurtling past them at 80% of the speed of light. As it goes by, the second hand on the ship's clock ticks off 5 seconds. How much time elapsed on the observer's clock during this occurrence?
A) more than 5 seconds if the spaceship is approaching the observer and less than 5 seconds if it is moving away from the observer
B) less than 5 seconds
C) more than 5 seconds
D) 5 seconds-the same as on the ship's clock

Accepted Answer

Due to the effects of time dilation in special relativity, time appears to move slower on the moving spaceship from the perspective of the stationary observer. Therefore, more than 5 seconds would elapse on the observer's clock while the spaceship's clock shows 5 seconds.

Question 4

If Alice stays on Earth while Bob races off in a rocket at a speed close to the speed of light, then, according to special relativity Alice will see a clock on the rocket appear to tick more slowly than the one on her wall. If Bob looks back at Alice's wall clock, then according to the same theory Bob will see the wall clock appear to tick
A) at the same speed as the clock on the rocket.
B) faster than the clock on the rocket.
C) faster or slower than the clock on the rocket, depending on the direction of travel of the rocket compared with Earth.
D) slower than the clock on the rocket.

Accepted Answer

According to the theory of special relativity, time dilation occurs for the observer in motion relative to a stationary observer. Thus, from Bob's perspective in the rocket, time on Earth (including Alice's wall clock) would appear to tick slower, just as Alice sees Bob's clock ticking slower. This reciprocal effect is a fundamental aspect of relativity, illustrating that each observer sees the other's clock as ticking slower.

Question 5

Two spaceships are traveling past Earth at 90% of the speed of light in opposite directions (i.e., they are approaching each other). One spaceship turns on a searchlight, which is seen by scientists aboard the other. What speed do the scientists measure for this light (c = speed of light in a vacuum)?
A) 1.9 c (equal to c + 0.9 c)
B) 1.8 c (equal to 2 *0.9 c).
C) c
D) 0.9 c

Accepted Answer

According to Einstein's theory of relativity, the speed of light in a vacuum is constant and does not depend on the speed of the observer or the source of the light. Therefore, regardless of the relative motion of the source and the observer, the scientists will measure the speed of light as c.

Question 6

Suppose a person is in a jet airliner traveling at a constant speed of 400 km/h in a constant direction. All windows are blocked, so they cannot see outside, and there are no vibrations from the engines. What experiment can be done to determine that they are in fact moving?
A) Suspend a ball by a thread from the ceiling and measure the angle the thread makes with the vertical.
B) None-all experiments will give the same results that one would get when at rest on the ground.
C) Measure the speed of a sound wave traveling up the aisle (toward the nose of the aircraft) and another traveling down toward the tail, and calculate the difference between the two results.
D) Drop a small rock and measure the distance it moves backward down the aisle as it falls.

Accepted Answer

Given the conditions described (constant velocity, no external reference points, and no vibrations), all experiments conducted inside the jet airliner would yield results indistinguishable from those obtained if the plane were at rest. This is because, according to the principle of relativity, the laws of physics are the same in all inertial frames of reference, which includes both a stationary environment and one moving at constant velocity in a straight line.

Question 7

In a TV tube, the picture is created by a beam of electrons that travels down the tube at a very high speed. What is the mass of one of these electrons, compared with an electron at rest?
A) The mass of an electron is measured to be the same regardless of how fast it is moving.
B) The moving electron appears to have a smaller mass.
C) The electron appears to have a greater mass if one is in front of the tube (electrons approaching) and a smaller mass if one is standing behind the tube (electrons moving away).
D) The moving electron appears to have a greater mass.

Accepted Answer

According to the theory of relativity, as the speed of an object approaches the speed of light, its mass appears to increase from the perspective of an observer. This means that an electron moving at very high speeds, such as those in a TV tube, would appear to have a greater mass compared to an electron at rest.

Question 8

Einstein's theory of special relativity contains some very strange ideas such as time dilation (moving clocks run slow), length contraction (moving lengths are shorter), and lack of absolute simultaneity. What is the basis of these ideas?
A) New technologies allow more precise measurements of length and time than had been possible in Newton's era, and the theory had to be reworked to fit this new evidence.
B) The speed of light is the same for all observers in all reference frames.
C) The ether (the medium that supports the passage of light) proved to be denser than originally thought.
D) The fabric of spacetime is dominated by black holes.

Accepted Answer

The basis of these ideas in Einstein's theory of special relativity is that the speed of light is constant for all observers, regardless of the motion of the light source or observer. This principle leads to the phenomena of time dilation, length contraction, and the lack of absolute simultaneity.

Question 9

A student is on Mars standing on the gangplank of a spaceship when she sees an identical spaceship go past Mars at 90% of the speed of light. When she looks closely at this spaceship, how does it compare with her own spaceship?
A) The moving spaceship appears to be shorter than hers, and time on it appears to move more slowly than on her ship.
B) The moving spaceship appears to be shorter than hers, and time on it appears to move more quickly than on her ship.
C) The moving spaceship appears to be longer than hers, and time on it appears to move more quickly than on her ship.
D) The moving spaceship appears to be longer than hers, and time on it appears to move more slowly than on her ship.

Accepted Answer

According to the theory of relativity, objects moving at a significant fraction of the speed of light will appear to contract in the direction of motion (length contraction) and time will appear to dilate, or move more slowly, from the perspective of a stationary observer.

Question 10

A bomb is attached to a timer and set to explode after exactly 10 seconds. This bomb is launched at half the speed of light relative to an observer. How much time will pass for the observer before the bomb explodes?
A) less than 10 seconds
B) more than 10 seconds
C) exactly 10 seconds
D) This is impossible to answer, as it depends on the direction in which the bomb is launched.

Accepted Answer

Due to the effects of time dilation as described by Einstein's theory of relativity, time will appear to pass more slowly for objects moving at a significant fraction of the speed of light relative to an observer. Therefore, the observer will see the bomb's timer take more than 10 seconds to reach zero.

Question 11

A clock is moving across an observer's line of sight with its face turned toward the observer. Which of these statements about this clock, as seen by the observer, is correct?
A) The clock will run slow compared with a clock in the observer's hand.
B) The clock will appear longer than it would if it were at rest.
C) The clock will appear thicker, front to back, than it would if it were at rest.
D) The clock will appear less massive than it would if it were at rest.

Accepted Answer

According to the theory of relativity, a moving clock appears to run slower compared to a stationary clock from the perspective of an observer. This phenomenon is known as time dilation.

Question 12

A clock with a luminous dial is moving toward an observer at a speed that is a large fraction of the speed of light. Which of these will the observer measure?
A) The light emitted by the clock will be shifted toward longer wavelengths compared to those seen by an observer moving with the clock.
B) The light from the clock is approaching the observer at speed c.
C) The clock runs fast compared to an identical clock at rest in the observer's hand.
D) The clock appears thicker, front to back, than the identical clock in observer's hand.

Accepted Answer

The speed of light in a vacuum is constant and does not change regardless of the relative motion of the source and the observer. This principle is a cornerstone of Einstein's theory of relativity, indicating that the light from the clock approaches the observer at speed c, the speed of light in a vacuum.

Question 13

Which of these statements is NOT a consequence of the postulates of special relativity?
A) The mass of an object moving with respect to an observer is larger than the mass measured by a different observer who is at rest with respect to the object.
B) A clock moving with respect to an observer ticks more slowly than when measured by an observer who is moving along with the clock.
C) The length of an object moving with respect to an observer is shorter than it is when measured by a different observer moving along with the object.
D) The wavelength emitted from a source moving with respect to an observer is different from the wavelength measured by an observer who is moving along with the source.

Accepted Answer

The answer of Which of these statements is NOT a...

Question 14

A spacecraft has a length of 2 meters if it is measured at rest. The spacecraft moves past an observer at half the speed of light. What will the observer measure the spacecraft's length to be?
A) less than 10 meters
B) more than 10 meters
C) exactly 10 meters
D) The answer will depend on whether the observer measures the length while it is moving toward or away from them.

Accepted Answer

The answer of A spacecraft has a length of 2...

Question 15

If an observer sees an object moving past them at 90% of the speed of light, what will its length appear to be?
A) The object will look longer than if it were at rest.
B) The object will look shorter than if it were at rest.
C) The object will look shorter than if it were at rest while it is coming toward them and longer after it has passed them.
D) The length of the object will appear to be unchanged from when it is at rest since it is a solid object.

Accepted Answer

According to the theory of relativity, objects moving at a significant fraction of the speed of light will appear contracted in the direction of motion to a stationary observer. This phenomenon is known as length contraction.

Question 16

Suppose an astronaut is aboard a spaceship that is passing Earth at 80% of the speed of light. The astronaut sees a clock on Earth tick off 5 seconds. How much time elapses on the astronaut's own clock while this is happening?
A) 5 seconds-the same as on the ship's clock
B) more than 5 seconds
C) more than 5 seconds if the astronaut is approaching Earth and less than 5 seconds if the astronaut is moving away from Earth
D) less than 5 seconds

Accepted Answer

The answer of Suppose an astronaut is aboard a spaceship...

Question 17

Suppose astronauts are in a spaceship traveling toward Earth at 95% of the speed of light. Compared with when the ship was at rest on Mars, what length do the astronauts measure for their spaceship?
A) It cannot be determined; their life processes have slowed down too much for them to measure the length.
B) same
C) shorter
D) longer

Accepted Answer

According to the theory of relativity, the length of an object as measured by an observer moving with the object is the same as its rest length. The astronauts are in the same inertial frame as their spaceship, so they would measure the spaceship to be the same length as when it was at rest.

Question 18

Which of these is a correct and complete statement of Einstein's first postulate of special relativity?
A) One's description of physical reality is the same regardless of the constant velocity at which one moves.
B) One's description of physical reality is the same regardless of the direction in which one moves, even if the speed changes.
C) One's description of physical reality is the same regardless of how one moves.
D) One's description of physical reality is the same regardless of the constant speed at which one moves, even if direction changes.

Accepted Answer

Einstein's first postulate of special relativity, also known as the principle of relativity, states that the laws of physics are the same in all inertial frames of reference, which means they hold for all observers moving at constant velocities relative to each other. Option A correctly captures this essence by stating that one's description of physical reality is the same regardless of the constant velocity at which one moves, implicitly including both speed and direction in the term "velocity."

Question 19

Suppose an astronaut is in the Space Shuttle in orbit around Earth at a speed of 7 km/s, and at some particular time the direction of travel is straight toward the Sun. The speed of light in a vacuum is 300,000 km/s. What speed will the astronaut measure for light from the Sun?
A) 300,007 km/s because the speed is added to that of the light
B) 300,014 km/s because the speed is added to that of the light, and relativistic contraction has shortened the meterstick used in the measurement of the speed of the light
C) 300,007 km/s because relativistic contraction has shortened the meterstick with which is measured the distance traveled by the light in order to measure its speed
D) 300,000 km/s

Accepted Answer

According to the theory of relativity, the speed of light in a vacuum is always measured as the same value, 300,000 km/s, regardless of the motion of the source or the observer.

Question 20

A child on a playground swing is swinging back and forth (one complete oscillation) once every 4 seconds, as seen by her father standing next to the swing. At the same time, a spaceship is hurtling by at a speed close to the speed of light. According to special relativity (and ignoring the Doppler effect for this question), her mother on the spaceship finds that the time for one full swing is
A) less than 4 seconds when the spaceship is approaching the swing and more than 4 seconds when it is moving away.
B) less than 4 seconds.
C) equal to 4 seconds.
D) more than 4 seconds.

Accepted Answer

Time dilation, a consequence of special relativity, implies that a moving observer (the mother in the spaceship) will measure a stationary process (the child swinging) to take longer than an observer at rest with respect to the process (the father).

Quiz 15: Black Holes: Matters of Gravity

What happens to the density of an object as it moves with respect to an observer as compared to the same object at rest with respect to the same observer?

Suppose an observer sees a spaceship with a clock on it hurtling past them at 80% of the speed of light. As it goes by, the second hand on the ship's clock ticks off 5 seconds. How much time elapsed on the observer's clock during this occurrence?

Suppose a person is in a jet airliner traveling at a constant speed of 400 km/h in a constant direction. All windows are blocked, so they cannot see outside, and there are no vibrations from the engines. What experiment can be done to determine that they are in fact moving?

In a TV tube, the picture is created by a beam of electrons that travels down the tube at a very high speed. What is the mass of one of these electrons, compared with an electron at rest?

Einstein's theory of special relativity contains some very strange ideas such as time dilation (moving clocks run slow) , length contraction (moving lengths are shorter) , and lack of absolute simultaneity. What is the basis of these ideas?

A student is on Mars standing on the gangplank of a spaceship when she sees an identical spaceship go past Mars at 90% of the speed of light. When she looks closely at this spaceship, how does it compare with her own spaceship?

A bomb is attached to a timer and set to explode after exactly 10 seconds. This bomb is launched at half the speed of light relative to an observer. How much time will pass for the observer before the bomb explodes?

A clock is moving across an observer's line of sight with its face turned toward the observer. Which of these statements about this clock, as seen by the observer, is correct?

A clock with a luminous dial is moving toward an observer at a speed that is a large fraction of the speed of light. Which of these will the observer measure?

Which of these statements is NOT a consequence of the postulates of special relativity?

A spacecraft has a length of 2 meters if it is measured at rest. The spacecraft moves past an observer at half the speed of light. What will the observer measure the spacecraft's length to be?

If an observer sees an object moving past them at 90% of the speed of light, what will its length appear to be?

Suppose an astronaut is aboard a spaceship that is passing Earth at 80% of the speed of light. The astronaut sees a clock on Earth tick off 5 seconds. How much time elapses on the astronaut's own clock while this is happening?

Suppose astronauts are in a spaceship traveling toward Earth at 95% of the speed of light. Compared with when the ship was at rest on Mars, what length do the astronauts measure for their spaceship?

Which of these is a correct and complete statement of Einstein's first postulate of special relativity?

Suppose an astronaut is in the Space Shuttle in orbit around Earth at a speed of 7 km/s, and at some particular time the direction of travel is straight toward the Sun. The speed of light in a vacuum is 300,000 km/s. What speed will the astronaut measure for light from the Sun?