Question 1

Two independent events occur 100 m apart with an intervening time interval of 0.42 $\mu$s.The proper time between the events is:

Accepted Answer

A) 0 $\mu$s 
B) 0.16 $\mu$s 
C) 0.26 $\mu$s 
D) 0.42 $\mu$s 
E) 0.69 $\mu$s 
A) 0 $\mu$s 
B) 0.16 $\mu$s 
C) 0.26 $\mu$s 
D) 0.42 $\mu$s 
E) 0.69 $\mu$s C

Question 2

A clock is moving along the x axis at 0.6c.It reads zero as it passes the origin (x = 0).When it passes the x = 180 m mark on the x axis the clock reads:

Accepted Answer

A) 0.60 $\mu$s 
B) 0.80 $\mu$s 
C) 1.00 $\mu$s 
D) 1.25 $\mu$s 
E) 1.67 $\mu$s 
A) 0.60 $\mu$s 
B) 0.80 $\mu$s 
C) 1.00 $\mu$s 
D) 1.25 $\mu$s 
E) 1.67 $\mu$s B

Question 3

A consequence of Einstein's theory of relativity is:

Accepted Answer

A) moving clocks appear to run faster than when they are at rest 
B) moving rods appear shorter than when they are at rest 
C) light has both wave and particle properties 
D) the laws of physics must appear the same to all observers moving with uniform velocity relative to each other 
E) everything is relative 
A) moving clocks appear to run faster than when they are at rest 
B) moving rods appear shorter than when they are at rest 
C) light has both wave and particle properties 
D) the laws of physics must appear the same to all observers moving with uniform velocity relative to each other 
E) everything is relative B

Question 4

Visible light, with a frequency of 6.0 *1014 Hz, is reflected from a spaceship moving directly away at a speed of 0.90c.The frequency of the reflected waves observed at the source is:

Accepted Answer

A) 3.2 * 1013 Hz 
B) 1.4 * 1014 Hz 
C) 6.0 * 1014 Hz 
D) 2.6 * 1015 Hz 
E) 1.1 * 1016 Hz 
A) 3.2 * 1013 Hz 
B) 1.4 * 1014 Hz 
C) 6.0 * 1014 Hz 
D) 2.6 * 1015 Hz 
E) 1.1 * 1016 Hz

Question 5

Which statement is correct?

Accepted Answer

A) Galilean transformations are correct at any relative speed, but Lorentz transformations are only approximately correct for relative speeds near the speed of light. 
B) Lorentz transformations are correct at any relative speed, but Galilean transformations are only approximately correct for relative speeds near the speed of light. 
C) Galilean transformations are correct at any relative speed, but Lorentz transformations are only approximately correct for relative speeds that are small compared to the speed of light. 
D) Lorentz transformations are correct at any relative speed, but Galilean transformations are only approximately correct for relative speeds that are small compared to the speed of light. 
E) Galilean transformations are only approximately correct for relative speeds that are small compared to the speed of light, and Lorentz transformations are only approximately correct for relative speeds near the speed of light. 
A) Galilean transformations are correct at any relative speed, but Lorentz transformations are only approximately correct for relative speeds near the speed of light. 
B) Lorentz transformations are correct at any relative speed, but Galilean transformations are only approximately correct for relative speeds near the speed of light. 
C) Galilean transformations are correct at any relative speed, but Lorentz transformations are only approximately correct for relative speeds that are small compared to the speed of light. 
D) Lorentz transformations are correct at any relative speed, but Galilean transformations are only approximately correct for relative speeds that are small compared to the speed of light. 
E) Galilean transformations are only approximately correct for relative speeds that are small compared to the speed of light, and Lorentz transformations are only approximately correct for relative speeds near the speed of light.

Question 6

As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9.0 * 10-8 s later a mark is made on the axis at the back end.The marks are 100 m apart.The rest length of the rocket is:

Accepted Answer

A) 31 m 
B) 78 m 
C) 100 m 
D) 240 m 
E) 320 m 
A) 31 m 
B) 78 m 
C) 100 m 
D) 240 m 
E) 320 m

Question 7

Star S1 is moving away from us at a speed of 0.8c.Star S2 is moving away from us in the opposite direction at a speed of 0.5c.The speed of S1 as measured by an observer on S2 is:

Accepted Answer

A) 0.21c 
B) 0.50c 
C) 0.93c 
D) 1.3c 
E) 2.2c 
A) 0.21c 
B) 0.50c 
C) 0.93c 
D) 1.3c 
E) 2.2c

Question 8

Spaceship A, traveling past us at 0.7c, sends a message capsule to spaceship B, which is in front of A and is traveling in the same direction as A at 0.8c relative to us.The capsule travels at 0.95c relative to us.A clock that measures the proper time between the sending and receiving of the capsule travels:

Accepted Answer

A) in the same direction as the spaceships at 0.7c relative to us 
B) in the opposite direction from the spaceships at 0.7c relative to us 
C) in the same direction as the spaceships at 0.8c relative to us 
D) in the same direction as the spaceships at 0.95c relative to us 
E) in the opposite direction from the spaceships at 0.95c relative to us 
A) in the same direction as the spaceships at 0.7c relative to us 
B) in the opposite direction from the spaceships at 0.7c relative to us 
C) in the same direction as the spaceships at 0.8c relative to us 
D) in the same direction as the spaceships at 0.95c relative to us 
E) in the opposite direction from the spaceships at 0.95c relative to us

Question 9

A train traveling very fast (v = 0.6c)has an engineer (E)at the front, a guard (G)at the rear and an observer (S')exactly half way between them.Both E and G are equipped with yellow signaling lamps.The train passes a station, closely observed by the station master (S).Both E and G use their lamps to send signals.According to both S and S' these signals arrive simultaneously at the instant S' is passing S.According to S':

Accepted Answer

A) E and G sent their signals simultaneously from different distances 
B) G sent his signal before E and from further away 
C) G sent his signal before E but was the same distance away 
D) E sent his signal before G and from further away 
E) none of the above 
A) E and G sent their signals simultaneously from different distances 
B) G sent his signal before E and from further away 
C) G sent his signal before E but was the same distance away 
D) E sent his signal before G and from further away 
E) none of the above

Question 10

A measurement of the length of an object that is moving relative to the laboratory consists of noting the coordinates of the front and back:

Accepted Answer

A) at different times according to clocks at rest in the laboratory 
B) at the same time according to clocks that move with the object 
C) at the same time according to clocks at rest in the laboratory 
D) at the same time according to clocks at rest with respect to the fixed stars 
E) none of the above 
A) at different times according to clocks at rest in the laboratory 
B) at the same time according to clocks that move with the object 
C) at the same time according to clocks at rest in the laboratory 
D) at the same time according to clocks at rest with respect to the fixed stars 
E) none of the above

Question 11

A meter stick moves in the direction of its length through a laboratory.According to measurements taken in the laboratory, its length is 0.31 m.The speed of the meter stick relative to the laboratory is:

Accepted Answer

A) 0.096c 
B) 0.31c 
C) 0.69c 
D) 0.83c 
E) 0.95c 
A) 0.096c 
B) 0.31c 
C) 0.69c 
D) 0.83c 
E) 0.95c

Question 12

A basic postulate of Einstein's theory of relativity is:

Accepted Answer

A) moving clocks run more slowly than when they are at rest 
B) moving rods are shorter than when they are at rest 
C) light has both wave and particle properties 
D) the laws of physics must be the same for observers moving with uniform velocity relative to each other 
E) everything is relative 
A) moving clocks run more slowly than when they are at rest 
B) moving rods are shorter than when they are at rest 
C) light has both wave and particle properties 
D) the laws of physics must be the same for observers moving with uniform velocity relative to each other 
E) everything is relative

Question 13

The proper time between two events is measured by clocks at rest in a reference frame in which the two events:

Accepted Answer

A) occur at the same time 
B) occur at the same coordinates 
C) are separated by the distance a light signal can travel during the time interval 
D) occur on the Earth's surface 
E) none of the above 
A) occur at the same time 
B) occur at the same coordinates 
C) are separated by the distance a light signal can travel during the time interval 
D) occur on the Earth's surface 
E) none of the above

Question 14

A train traveling very fast (v = 0.6c)has an engineer (E)at the front, a guard (G)at the rear and a passenger (S')exactly half way between them.Both E and G are equipped with yellow signaling lamps.The train passes a station, closely observed by the station master (S).Both E and G use their lamps to send signals.According to both S and S' these signals arrive simultaneously at the instant S' is passing S.According to S, the signal from E will look ______ and that from G will look _____:

Accepted Answer

A) red, blue 
B) yellow, yellow 
C) blue, red 
D) blue, blue 
E) red, red 
A) red, blue 
B) yellow, yellow 
C) blue, red 
D) blue, blue 
E) red, red

Question 15

How fast should you move away from a 6.0 *1014 Hz light source to observe waves with a frequency of 4.0 * 1014 Hz?

Accepted Answer

A) 0.20c 
B) 0.39c 
C) 0.45c 
D) 0.51c 
E) 0.76c 
A) 0.20c 
B) 0.39c 
C) 0.45c 
D) 0.51c 
E) 0.76c

Question 16

According to relativity theory a particle of mass m with a momentum of 2mc has a speed of:

Accepted Answer

A) 4c 
B) 2c 
C) c 
D) 0.89c 
E) c/2 
A) 4c 
B) 2c 
C) c 
D) 0.89c 
E) c/2

Question 17

The velocity of an electron is changed from c/2 in the -x direction to c/2 in the +x direction.As a result, its kinetic energy changes by:

Accepted Answer

A) 2mc2 
B) √2mc2 
C) mc2 
D) 0.5mc2 
E) 0 
A) 2mc2 
B) √2mc2 
C) mc2 
D) 0.5mc2 
E) 0

Question 18

A spectral line of a certain star is observed to be "red shifted" from a wavelength of 500 nm to a wavelength of 1500 nm.Interpreting this as a Doppler effect, the speed of recession of this star is:

Accepted Answer

A) 0.33c 
B) 0.50c 
C) 0.71c 
D) 0.80c 
E) c 
A) 0.33c 
B) 0.50c 
C) 0.71c 
D) 0.80c 
E) c

Question 19

The spaceship U.S.S.Enterprise, traveling through the galaxy, sends out a smaller explorer craft that travels to a nearby planet and signals its findings back.The proper time for the trip to the planet is measured by clocks:

Accepted Answer

A) on board the Enterprise 
B) on board the explorer craft 
C) on Earth 
D) at the center of the galaxy 
E) none of the above 
A) on board the Enterprise 
B) on board the explorer craft 
C) on Earth 
D) at the center of the galaxy 
E) none of the above

Question 20

If the kinetic energy of a free particle is much greater than its rest energy then its kinetic energy is proportional to:

Accepted Answer

A) the magnitude of its momentum 
B) the square of the magnitude of its momentum 
C) the square root of the magnitude of its momentum 
D) the reciprocal of the magnitude of its momentum 
E) none of the above 
A) the magnitude of its momentum 
B) the square of the magnitude of its momentum 
C) the square root of the magnitude of its momentum 
D) the reciprocal of the magnitude of its momentum 
E) none of the above

Exam 37: Relativity

Two independent events occur 100 m apart with an intervening time interval of 0.42 μ\muμ s.The proper time between the events is:

A clock is moving along the x axis at 0.6c.It reads zero as it passes the origin (x = 0).When it passes the x = 180 m mark on the x axis the clock reads:

A consequence of Einstein's theory of relativity is:

Visible light, with a frequency of 6.0 *1014 Hz, is reflected from a spaceship moving directly away at a speed of 0.90c.The frequency of the reflected waves observed at the source is:

Which statement is correct?

As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9.0 * 10-8 s later a mark is made on the axis at the back end.The marks are 100 m apart.The rest length of the rocket is:

Star S1 is moving away from us at a speed of 0.8c.Star S2 is moving away from us in the opposite direction at a speed of 0.5c.The speed of S1 as measured by an observer on S2 is:

A measurement of the length of an object that is moving relative to the laboratory consists of noting the coordinates of the front and back:

A meter stick moves in the direction of its length through a laboratory.According to measurements taken in the laboratory, its length is 0.31 m.The speed of the meter stick relative to the laboratory is:

A basic postulate of Einstein's theory of relativity is:

The proper time between two events is measured by clocks at rest in a reference frame in which the two events:

How fast should you move away from a 6.0 *1014 Hz light source to observe waves with a frequency of 4.0 * 1014 Hz?

According to relativity theory a particle of mass m with a momentum of 2mc has a speed of:

The velocity of an electron is changed from c/2 in the -x direction to c/2 in the +x direction.As a result, its kinetic energy changes by:

A spectral line of a certain star is observed to be "red shifted" from a wavelength of 500 nm to a wavelength of 1500 nm.Interpreting this as a Doppler effect, the speed of recession of this star is:

The spaceship U.S.S.Enterprise, traveling through the galaxy, sends out a smaller explorer craft that travels to a nearby planet and signals its findings back.The proper time for the trip to the planet is measured by clocks:

If the kinetic energy of a free particle is much greater than its rest energy then its kinetic energy is proportional to:

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Two independent events occur 100 m apart with an intervening time interval of 0.42 $\mu$ s.The proper time between the events is:

Visible light, with a frequency of 6.0 *10¹⁴ Hz, is reflected from a spaceship moving directly away at a speed of 0.90c.The frequency of the reflected waves observed at the source is:

As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9.0 * 10^-8 s later a mark is made on the axis at the back end.The marks are 100 m apart.The rest length of the rocket is:

How fast should you move away from a 6.0 10¹⁴ Hz light source to observe waves with a frequency of 4.0 10¹⁴ Hz?