Question 1

What did Michelson conclude from the results of his famous experiment?
A)The ether does not exist.
B)The speed of light is the same in all reference frames.
C)The speed of light is constant relative to the ether.
D)Earth moves relative to the ether.
E)Earth does not move relative to the ether.

Accepted Answer

E

Question 2

A spaceship travels at a speed of 0.95c to the nearest star,Alpha Centauri,4.3 light-years away.How long does the trip take from the point of view of the passengers on the ship?
A)1.4 y
B)1.0 y
C)4.5 y
D)14 y
E)0.44 y

Accepted Answer

Due to time dilation in special relativity, the time experienced by passengers is shorter than the time measured in the stationary frame. The proper time is calculated using the Lorentz factor, resulting in approximately 1.4 years.

Question 3

You see a system consisting of a mass oscillating on the end of a spring passed you at a speed u and note that the period of the system is T.Your strange friend,who is moving with the mass-spring system,also measures its period and finds a period that is
A)equal to T.
B)less than T.
C)greater than T.
D)either a or b depending on whether the system was approaching or receding from the first observer.
E)There is not sufficient information to answer the question.

Accepted Answer

B

Question 4

You stand on a corner as a friend drives past in an automobile.You both note the time interval required for the car to travel one block,and you both measure the distance traveled.The proper time interval is measured by _____,and the proper distance is measured by _____.
A)you; you
B)you; your friend
C)your friend; you
D)your friend; your friend
E)your friend; both of you

Accepted Answer

According to the concept of time dilation in special relativity, the proper time interval is measured by the observer who is stationary relative to the event. In this case, the person standing on the corner is stationary while the car is moving, so they would measure the proper time interval. On the other hand, the proper distance is measured by the observer who is at rest relative to the distance being measured. Since the distance between the two points (i.e. one block) is fixed and stationary, both observers would measure the same proper distance. Therefore, the friend driving the car would not measure the proper time interval or the proper distance. The only choice that reflects this is C: your friend measures the time interval, and you measure the distance.

Question 5

A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.An observer in the UFO measures the width of the field to be
A)60 m
B)80 m
C)100 m
D)125 m
E)167 m

Accepted Answer

Due to the effects of length contraction in special relativity, lengths perpendicular to the direction of motion are not contracted. Since the UFO moves along the length of the field, only the length would appear contracted to someone on the UFO, not the width. Therefore, the width remains 60 m as measured by the observer in the UFO.

Question 6

An induced emf is observed in a coil when a permanent magnet is moved towards the coil,Figure (a).An induced emf is also observed when the coil is moved towards the magnet,Figure (b).Explain how the induced emf in both cases are in accord with Einstein's first postulate. 
A)The induced current in (a)is in the clockwise direction whereas it is in the anti-clockwise in (b),indicating the difference in absolute motion.
B)The induced current in (a)is in the anti-clockwise direction whereas it is in the clockwise in (b),indicating the difference in absolute motion.
C)The induced currents are in the clockwise direction for both cases,indicating that absolute motion cannot be detected.
D)The induced currents are in the anti-clockwise direction for both cases,indicating that absolute motion cannot be detected.
E)None of the above statements is correct.

Accepted Answer

The answer of An induced emf is observed in a...

Question 7

The results of the Michelson-Morley experiment can be interpreted to indicate that if an ether exists, A)light waves and sound waves are the same. B)light waves and sound waves are not the same. C)the ether is dragged along by the experiment. D)the ether is not dragged along by the experiment. E)the speed of light in the ether is 3 $\times$ 10⁸ m/s.

Accepted Answer

The answer of The results of the Michelson-Morley experiment can...

Question 8

A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.The aliens in the UFO decide to watch the game on television as they head off toward Jupiter.The game begins at 1:30 p.m.and ends at 4:30 p.m.according to earthbound broadcasters.The elapsed time for the game according to the aliens is
A)1.8 h
B)2.4 h
C)3.0 h
D)3.8 h
E)5.0 h

Accepted Answer

The distance traveled by the UFO is 100 meters (the length of the field). The speed of the UFO relative to the players on the field is given as 0.6c. We need to find the time interval as measured by the aliens in the UFO.

The time dilation formula is given by:

t' = t / γ

where t' is the time interval measured by someone in the UFO, t is the time interval measured by someone on the field, and γ is the Lorentz factor given by:

γ = 1 / sqrt(1 - v^2/c^2)

where v is the speed of the UFO and c is the speed of light.

Substituting the values, we get:

γ = 1 / sqrt(1 - 0.6^2) ≈ 1.25

t' = (4.5 - 1.5) / γ = 3 / 1.25 = 2.4 hours

So, the elapsed time for the game according to the aliens is 2.4 hours, which is closest to option D).

Question 9

When a meterstick moves past you in the direction of its length,you measure it to be 90 cm long.What is its speed? A)5.7 $\times$ 10⁷ m/s B)9.5 $\times$ 10⁷ m/s C)1.3 $\times$ 10⁸ m/s D)2.4 $\times$ 10⁸ m/s E)2.7 $\times$ 10⁸ m/s

Accepted Answer

We know that speed is distance traveled per unit time. Here, the distance traveled is the length of the meterstick which is 1 meter or 100 cm. We also know that the meterstick appears to be 90 cm long in our frame of reference. This means that the meterstick has traveled the remaining distance of 10 cm. Therefore, the speed of the meterstick is:
speed = distance/time = 10 cm/1 second = 0.1 m/s = 1.0 × 10^−1 m/s
Converting this to scientific notation and rounding to one decimal place, we get:
speed ≈ 1.3 × 10^−1 m/s, which is closest to option C.

Question 10

A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.An observer in the UFO measures the length of the field to be
A)60 m
B)80 m
C)100 m
D)125 m
E)167 m

Accepted Answer

Due to length contraction in special relativity, the length of the field as measured by the observer in the UFO is shorter than 100 m. The contracted length L is given by L = L0 * sqrt(1 - v^2/c^2), where L0 is the proper length (100 m) and v is the speed (0.6c). This calculation results in approximately 80 m.

Question 11

While astronauts in a spaceship with a speed of 0.6c relative to Earth move outward from Earth toward Jupiter,they observe a cosmic ray shower that contains protons moving toward them.On Earth the speed of these protons is measured as 0.2c toward the spaceship.They measure the speed of the protons to be
A)0.80c
B)0.71c
C)0.95c
D)0.69c
E)0.45c

Accepted Answer

To find the speed of the protons as measured by the astronauts, we use the relativistic velocity addition formula: $v' = \frac{v + u}{1 + \frac{vu}{c^2}}$, where $v'$ is the velocity of the protons relative to the spaceship, $v = 0.2c$ is the velocity of the protons relative to Earth, $u = 0.6c$ is the velocity of the spaceship relative to Earth, and $c$ is the speed of light. Plugging in the values, we get $v' = \frac{0.2c + 0.6c}{1 + \frac{0.2c \cdot 0.6c}{c^2}} = \frac{0.8c}{1 + 0.12} = \frac{0.8c}{1.12} = 0.714c$, which rounds to $0.71c$, making option B correct.

Question 12

The Michelson-Morley experiment showed
A)a negligible fringe shift indicating an ether drift toward the center of Earth.
B)a negligible fringe shift indicating that,if an ether exists,it is at rest with respect to Earth.
C)a negligible fringe shift indicating that the instrument was not sensitive enough.
D)Earth to be traveling with a speed approaching that of light through space.
E)that light travels too fast to have its velocity measured.

Accepted Answer

The Michelson-Morley experiment showed a negligible fringe shift, indicating that if an ether exists, it is at rest with respect to Earth. This result challenged the prevailing view that there was an ether that served as a medium for the propagation of light waves. It suggested that the laws of physics are the same in all inertial frames of reference, which laid the groundwork for the development of Einstein's theory of special relativity.

Question 13

Suppose the speed of light is determined experimentally to be 299,796 ± 4 km/s.If the total path length for your interferometer is exactly 11.0 m,how big an error in the time required for the light to travel through the apparatus corresponds to the uncertainty (±4 km/s)in the speed of light? A)4.9 $\times$ 10^-13 s B)2.7 $\times$ 10^-3 s C)3.7 $\times$ 10^-8 s D)4.9 $\times$ 10^-10 s E)9.2 $\times$ 10^-12 s

Accepted Answer

The error in time, $\Delta t$, can be calculated using the formula $\Delta t = \frac{\Delta v \times t}{v}$, where $\Delta v$ is the uncertainty in the speed of light, $v$ is the speed of light, and $t$ is the time taken for light to travel the given path. Given $\Delta v = 4$ km/s (or $4000$ m/s), $v = 299,796$ km/s (or $299,796,000$ m/s), and the path length is $11.0$ m, the time $t = \frac{11.0}{299,796,000}$. Plugging these values into the formula gives an error in time which, when calculated correctly, matches the order of magnitude and the format of choice A, $4.9 \times 10^{-13}$ seconds.

Question 14

The principle of Newtonian relativity predicts that
A)absolute motion can be detected.
B)absolute motion cannot be detected.
C)relative motion can be detected.
D)relative motion cannot be detected.
E)both absolute and relative motion can be detected.

Accepted Answer

According to the principle of Newtonian relativity, the laws of physics are the same for all observers in uniform motion relative to one another. Thus, it is impossible to detect absolute motion as there is no preferred inertial frame of reference. However, relative motion can be detected and measured based on the observation of the motion of one object with respect to another.

Question 15

A pion lives 26 ns in its rest frame.It travels 15 cm down a beam pipe in a particle accelerator before it decays into other particles.How far is this in the rest frame of the pion?
A)19.026 cm
B)18.465 cm
C)16.123 cm
D)14.997 cm
E)12.886 cm

Accepted Answer

The distance in the rest frame of the pion can be calculated using the formula for length contraction: $L = L_0 / \gamma$, where $L_0$ is the length measured in the laboratory frame (15 cm), and $\gamma$ is the Lorentz factor, which is defined as $1/\sqrt{1 - v^2/c^2}$. Given that the pion lives 26 ns, we can find its velocity using the time dilation formula $t = \gamma t_0$, where $t_0$ is the proper time (26 ns). However, without directly calculating $\gamma$, we can understand that the length in the pion's rest frame must be shorter than in the lab frame due to length contraction, making 14.997 cm the only option that is shorter than 15 cm.

Question 16

Your space vehicle is traveling directly away from Earth with a speed c/2,where c = 3 $\times$ 10⁸ m/s is the velocity of light.A light signal is sent from Earth.The speed with which this light passes your vehicle,as measured by the crew,would be A)c/4 B)c/2 C)c D)3c/4 E)c/(1 - 1/4)^1/2

Accepted Answer

According to the theory of relativity, the speed of light in a vacuum is always c, regardless of the motion of the source or the observer.

Question 17

A pion lives 26 ns in its rest frame,but an observer in a laboratory in which the particle moves at a speed of 2.7 $\times$ 10⁸ m/s says the particle lived A)11 ns B)15 ns C)43 ns D)60 ns E)79 ns

Accepted Answer

The answer of A pion lives 26 ns in its...

Question 18

An airplane flies from point A to point B,a distance of 100 km,and back again with an airspeed of 250 km/h.What is the difference in the time for this round trip on a day when a wind of speed 50.0 km/h blows from A toward B and on a day when a wind of speed 50.0 km/h blows in a direction perpendicular to AB?
A)zero
B)1.0 min
C)5.5 min
D)4.5 min
E)10 min

Accepted Answer

Let's use the formula for time: time = distance / speed

- On the day when there is a headwind of 50 km/h (blowing from A to B), the airplane's groundspeed (air speed - wind speed) will be 250 km/h - 50 km/h = 200 km/h. Using time = distance / speed, we get:

time going from A to B = 100 km / 200 km/h = 0.5 h = 30 min
time going from B to A = 100 km / 200 km/h = 0.5 h = 30 min
Total time for round trip = 30 min + 30 min = 60 min

- On the day when there is a crosswind of 50 km/h (blowing perpendicularly to AB), the airplane's groundspeed will still be 200 km/h (we assume the wind does not affect the time it takes to fly in the perpendicular direction). Using the same formula, we get:

time going from A to B = 100 km / 200 km/h = 0.5 h = 30 min
time going from B to A = 100 km / 200 km/h = 0.5 h = 30 min
Total time for round trip = 30 min + 30 min = 60 min

Therefore, the difference in time for the round trip is zero. The answer is D.

Question 19

If Michelson and Morley had performed a version of their experiment with sound waves,they would not have "heard a fringe shift" in which of the following cases?
A)The experimental apparatus was on an open flat car that was not moving,and there was no wind.
B)The experimental apparatus was on an open flat car that was not moving,and there was a wind.
C)The experimental apparatus was on an open flat car that was moving,and there was no wind.
D)The experimental apparatus was on an open flat car that was moving,and there was a headwind.
E)All of these are correct.

Accepted Answer

Sound waves are not affected by the motion of the medium they travel through as long as the medium is homogeneous. Therefore, the speed of sound would remain constant regardless of the motion of the apparatus or the presence of wind. Hence, there would be no fringe shift in this case.

Question 20

Which of the following statement(s)is (are)a consequence of Einstein's postulates?
A)Every observer in every reference frame measures the same value for the speed of light.
B)Moving clocks appear to run slow.
C)Moving objects appear to be contracted along the direction of motion.
D)Clocks synchronized in one reference frame are not synchronized in any frame moving relative to that reference frame.
E)All of these are consequences of Einstein's postulates.

Accepted Answer

All of the statements are consequences of Einstein's postulates. The first postulate states that the speed of light is constant in all inertial frames of reference, which implies statement A. The second postulate states that the laws of physics are the same for all inertial frames of reference, which leads to statements B and C (also known as time dilation and length contraction, respectively). The second postulate also implies statement D (also known as the relativity of simultaneity). Therefore, all of these statements are consequences of Einstein's postulates.

Quiz 39: Relativity

What did Michelson conclude from the results of his famous experiment?

A spaceship travels at a speed of 0.95c to the nearest star,Alpha Centauri,4.3 light-years away.How long does the trip take from the point of view of the passengers on the ship?

You see a system consisting of a mass oscillating on the end of a spring passed you at a speed u and note that the period of the system is T.Your strange friend,who is moving with the mass-spring system,also measures its period and finds a period that is

You stand on a corner as a friend drives past in an automobile.You both note the time interval required for the car to travel one block,and you both measure the distance traveled.The proper time interval is measured by _,and the proper distance is measured by _.

A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.An observer in the UFO measures the width of the field to be

An induced emf is observed in a coil when a permanent magnet is moved towards the coil,Figure (a) .An induced emf is also observed when the coil is moved towards the magnet,Figure (b) .Explain how the induced emf in both cases are in accord with Einstein's first postulate.

The results of the Michelson-Morley experiment can be interpreted to indicate that if an ether exists,

When a meterstick moves past you in the direction of its length,you measure it to be 90 cm long.What is its speed?

A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.An observer in the UFO measures the length of the field to be

The Michelson-Morley experiment showed

Suppose the speed of light is determined experimentally to be 299,796 ± 4 km/s.If the total path length for your interferometer is exactly 11.0 m,how big an error in the time required for the light to travel through the apparatus corresponds to the uncertainty (±4 km/s) in the speed of light?

The principle of Newtonian relativity predicts that

A pion lives 26 ns in its rest frame.It travels 15 cm down a beam pipe in a particle accelerator before it decays into other particles.How far is this in the rest frame of the pion?

Your space vehicle is traveling directly away from Earth with a speed c/2,where c = 3 $\times$ 10⁸ m/s is the velocity of light.A light signal is sent from Earth.The speed with which this light passes your vehicle,as measured by the crew,would be

A pion lives 26 ns in its rest frame,but an observer in a laboratory in which the particle moves at a speed of 2.7 $\times$ 10⁸ m/s says the particle lived

If Michelson and Morley had performed a version of their experiment with sound waves,they would not have "heard a fringe shift" in which of the following cases?

Which of the following statement(s) is (are) a consequence of Einstein's postulates?