Question 1

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)  0.5c 
C)  0.93c 
D)  1.3c 
E)  2.17c 
A)  0.21c 
B)  0.5c 
C)  0.93c 
D)  1.3c 
E)  2.17c C

Question 2

A certain particle has a kinetic energy of 3.2* 10-10 J and a momentum of 1.7 *10-18 kg . m/s. Its mass is:

Accepted Answer

A)  9.11 * 10-31 kg 
B)  2.7 *10-27 kg 
C)  4.5 * 10-27 kg 
D)  6.3 * 10-27 kg 
E)  8.6 * 10-27 kg 
A)  9.11 * 10-31 kg 
B)  2.7 *10-27 kg 
C)  4.5 * 10-27 kg 
D)  6.3 * 10-27 kg 
E)  8.6 * 10-27 kg B

Question 3

A console lamp in the cabin of a spaceship appears green when the ship and observer are both at rest. When the ship is moving at 0.90c away from Earth, passengers on board see:

Accepted Answer

A)  a dark lamp (the frequency is too high to be seen) 
B)  a dark lamp (the frequency is too low to be seen) 
C)  a red lamp 
D)  a violet lamp 
E)  a green lamp 
A)  a dark lamp (the frequency is too high to be seen) 
B)  a dark lamp (the frequency is too low to be seen) 
C)  a red lamp 
D)  a violet lamp 
E)  a green lamp B

Question 4

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 5

A meson moving through a laboratory of length x at a speed v decays after a lifetime T as measured by an observer at rest in the laboratory. If the meson were at rest in the laboratory its lifetime would be:

Accepted Answer

A)  T(1 - v/c) 
B)  T(1 - v/c)-1 
C)  T(1 - v2/c2)-1/2 
D)  T(1 - v2/c2)1/2 
E)  (T - vx/c2)(1 - v2/c2)-1/2 
A)  T(1 - v/c) 
B)  T(1 - v/c)-1 
C)  T(1 - v2/c2)-1/2 
D)  T(1 - v2/c2)1/2 
E)  (T - vx/c2)(1 - v2/c2)-1/2

Question 6

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 in Boston 
E)  satisfy 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 in Boston 
E)  satisfy none of the above

Question 7

An electron (m = 9.11 * 10-31 kg) has a speed of 0.95c. Its kinetic energy is:

Accepted Answer

A)  8.2 * 10-14 J 
B)  1.8 * 10-13 J 
C)  2.0 * 10-13 J 
D)  2.2 * 10-13 J 
E)  2.6 * 10-13 J 
A)  8.2 * 10-14 J 
B)  1.8 * 10-13 J 
C)  2.0 * 10-13 J 
D)  2.2 * 10-13 J 
E)  2.6 * 10-13 J

Question 8

An observer notices that a moving clock runs slow by a factor of exactly 10. The speed of the clock is:

Accepted Answer

A)  0.100c 
B)  0.0100c 
C)  0.990c 
D)  0.900c 
E)  0.995c 
A)  0.100c 
B)  0.0100c 
C)  0.990c 
D)  0.900c 
E)  0.995c

Question 9

An electron (m = 9.11 *10-31 kg) has a momentum of 4.0 *10-13 kg .m/s. Its kinetic energy is:

Accepted Answer

A)  6.3 *10-14 J 
B)  8.2 * 10-14 J 
C)  1.2* 10-13 J 
D)  1.5 * 10-13 J 
E)  2.7* 10-13 J 
A)  6.3 *10-14 J 
B)  8.2 * 10-14 J 
C)  1.2* 10-13 J 
D)  1.5 * 10-13 J 
E)  2.7* 10-13 J

Question 10

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 11

Observer A measures the velocity of a rocket as   and a comet as   . Here   are parallel and in the direction of the observer's positive x axis. The speed of the comet as measured by an observer on the rocket is:

Accepted Answer

A)  (u - v)/(1 - uv/c2) 
B)  (u - v)/(1 - v2/c2) 
C)  (u - v)/(1 - v2/c2)1/2 
D)  (u - v)/(1 + uv/c2) 
E)  (u + v)/(1 - uv/c2) 
A)  (u - v)/(1 - uv/c2) 
B)  (u - v)/(1 - v2/c2) 
C)  (u - v)/(1 - v2/c2)1/2 
D)  (u - v)/(1 + uv/c2) 
E)  (u + v)/(1 - uv/c2)

Question 12

A train traveling very fast (v = 0.6c) has an engineer (E) at the front, a guard (G) at the rear and an 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 13

As we watch, a spaceship passes us in time $\Delta$t. The crew of the spaceship measures the passage time and finds it to be $\Delta$t'. Which of the following statements is true?

Accepted Answer

A)  $\Delta$t is the proper time for the passage and it is smaller than $\Delta$t' 
B)  $\Delta$t is the proper time for the passage and it is greater than $\Delta$t' 
C)  $\Delta$t' is the proper time for the passage and it is smaller than $\Delta$t 
D)  $\Delta$t' is the proper time for the passage and it is greater than $\Delta$t 
E)  None of the above statements are true. 
A)  $\Delta$t is the proper time for the passage and it is smaller than $\Delta$t' 
B)  $\Delta$t is the proper time for the passage and it is greater than $\Delta$t' 
C)  $\Delta$t' is the proper time for the passage and it is smaller than $\Delta$t 
D)  $\Delta$t' is the proper time for the passage and it is greater than $\Delta$t 
E)  None of the above statements are true.

Question 14

A millionairess was told in 1992 that she had exactly 15 years to live. However, if she travels away from the Earth at 0.8 c and then returns at the same speed, the last New Year's day the doctors expect her to celebrate is:

Accepted Answer

A)  2001 
B)  2003 
C)  2007 
D)  2010 
E)  2017 
A)  2001 
B)  2003 
C)  2007 
D)  2010 
E)  2017

Question 15

A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c toward an observer, the observer detects light of wavelength:

Accepted Answer

A)  26 nm 
B)  115 nm 
C)  500 nm 
D)  2200 nm 
E)  9500 nm 
A)  26 nm 
B)  115 nm 
C)  500 nm 
D)  2200 nm 
E)  9500 nm

Question 16

An event occurs at x = 500 m, t = 0.90 $\mu$s in one frame of reference. Another frame is moving at 0.90c in the negative x direction. The origins coincide at t = 0 and clocks in the second frame are zeroed when the origins coincide. The coordinate and time of the event in the second frame is:

Accepted Answer

A)  500 m, 0.90 $\mu$s 
B)  1700 m, 5.5 $\mu$s 
C)  740 m, 2.4 $\mu$s 
D)  260 m, -0.60 $\mu$s 
E)  590 m, -1.4 $\mu$s 
A)  500 m, 0.90 $\mu$s 
B)  1700 m, 5.5 $\mu$s 
C)  740 m, 2.4 $\mu$s 
D)  260 m, -0.60 $\mu$s 
E)  590 m, -1.4 $\mu$s

Question 17

An event occurs at x = 500 m, t = 0.90 $\mu$s in one frame of reference. Another frame is moving at 0.90c in the positive x direction. The origins coincide at t = 0 and clocks in the second frame are zeroed when the origins coincide. The coordinate and time of the event in the second frame is:

Accepted Answer

A)  500 m, 0.90 $\mu$s 
B)  1700 m, 5.5 $\mu$s 
C)  740 m, 2.4 $\mu$s 
D)  260 m, -0.60 $\mu$s 
E)  590 m, -1.4 $\mu$s 
A)  500 m, 0.90 $\mu$s 
B)  1700 m, 5.5 $\mu$s 
C)  740 m, 2.4 $\mu$s 
D)  260 m, -0.60 $\mu$s 
E)  590 m, -1.4 $\mu$s

Question 18

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

Accepted Answer

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

Question 19

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 20

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

Exam 37: Relativity

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 certain particle has a kinetic energy of 3.2* 10-10 J and a momentum of 1.7 *10-18 kg . m/s. Its mass is:

A console lamp in the cabin of a spaceship appears green when the ship and observer are both at rest. When the ship is moving at 0.90c away from Earth, passengers on board see:

A meson moving through a laboratory of length x at a speed v decays after a lifetime T as measured by an observer at rest in the laboratory. If the meson were at rest in the laboratory its lifetime would be:

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

An electron (m = 9.11 * 10-31 kg) has a speed of 0.95c. Its kinetic energy is:

An observer notices that a moving clock runs slow by a factor of exactly 10. The speed of the clock is:

An electron (m = 9.11 *10-31 kg) has a momentum of 4.0 *10-13 kg .m/s. Its kinetic energy 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?

Observer A measures the velocity of a rocket as and a comet as . Here are parallel and in the direction of the observer's positive x axis. The speed of the comet as measured by an observer on the rocket is:

As we watch, a spaceship passes us in time Δ\DeltaΔ t. The crew of the spaceship measures the passage time and finds it to be Δ\DeltaΔ t'. Which of the following statements is true?

A millionairess was told in 1992 that she had exactly 15 years to live. However, if she travels away from the Earth at 0.8 c and then returns at the same speed, the last New Year's day the doctors expect her to celebrate is:

A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c toward an observer, the observer detects light of wavelength:

An event occurs at x = 500 m, t = 0.90 μ\muμ s in one frame of reference. Another frame is moving at 0.90c in the negative x direction. The origins coincide at t = 0 and clocks in the second frame are zeroed when the origins coincide. The coordinate and time of the event in the second frame is:

An event occurs at x = 500 m, t = 0.90 μ\muμ s in one frame of reference. Another frame is moving at 0.90c in the positive x direction. The origins coincide at t = 0 and clocks in the second frame are zeroed when the origins coincide. The coordinate and time of the event in the second frame is:

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

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:

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Motion in Two and Three Dimensions

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Rotation

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A certain particle has a kinetic energy of 3.2* 10^-¹⁰ J and a momentum of 1.7 *10^-¹⁸ kg . m/s. Its mass is:

An electron (m = 9.11 * 10^-³¹ kg) has a speed of 0.95c. Its kinetic energy is:

An electron (m = 9.11 10^-³¹ kg) has a momentum of 4.0 10^-¹³ kg .m/s. Its kinetic energy 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?

As we watch, a spaceship passes us in time $\Delta$ t. The crew of the spaceship measures the passage time and finds it to be $\Delta$ t'. Which of the following statements is true?

An event occurs at x = 500 m, t = 0.90 $\mu$ s in one frame of reference. Another frame is moving at 0.90c in the negative x direction. The origins coincide at t = 0 and clocks in the second frame are zeroed when the origins coincide. The coordinate and time of the event in the second frame is:

An event occurs at x = 500 m, t = 0.90 $\mu$ s in one frame of reference. Another frame is moving at 0.90c in the positive x direction. The origins coincide at t = 0 and clocks in the second frame are zeroed when the origins coincide. The coordinate and time of the event in the second frame is: