Question 1

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 * 108 m/s says the particle lived

Accepted Answer

A)  11 ns 
B)  15 ns 
C)  43 ns 
D)  60 ns 
E)  79 ns 
A)  11 ns 
B)  15 ns 
C)  43 ns 
D)  60 ns 
E)  79 ns D

Question 2

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

Accepted Answer

A)  0.80c 
B)  0.71c 
C)  0.95c 
D)  0.69c 
E)  0.45c 
A)  0.80c 
B)  0.71c 
C)  0.95c 
D)  0.69c 
E)  0.45c B

Question 3

Einstein's Second Postulate states that nothing can travel faster than the speed of light. The kinetic energy of a particle of rest mass m

Accepted Answer

A)  has an upper limit of mc2. 
B)  has an upper limit of   mc2. 
C)  has an upper limit of 2mc2. 
D)  is infinite as the speed approaches c. 
E)  none of the above 
A)  has an upper limit of mc2. 
B)  has an upper limit of   mc2. 
C)  has an upper limit of 2mc2. 
D)  is infinite as the speed approaches c. 
E)  none of the above D

Question 4

The Sun radiates electromagnetic energy at the rate of 3.92 * 1026 W. What is the change in the Sun's mass during each second that it is radiating energy?

Accepted Answer

A)  1.31 * 1018 kg 
B)  4.36 * 109 kg 
C)  3.15 * 106 kg 
D)  7.18 *108 kg 
E)  None of these is correct. 
A)  1.31 * 1018 kg 
B)  4.36 * 109 kg 
C)  3.15 * 106 kg 
D)  7.18 *108 kg 
E)  None of these is correct.

Question 5

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c. An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min). The time between beats according to a sympathetic astronaut aboard Klara is

Accepted Answer

A)  0.00800 min 
B)  0.0106 min 
C)  0.0133 min 
D)  0.0166 min 
E)  0.0222 min 
A)  0.00800 min 
B)  0.0106 min 
C)  0.0133 min 
D)  0.0166 min 
E)  0.0222 min

Question 6

The energy released by the nuclear bomb that destroyed Hiroshima was equivalent to 12.4 kilotons of TNT. This is equivalent to 9.0 * 1026 MeV. The mass that was converted into energy in this explosion was

Accepted Answer

A)  1.6 kg 
B)  1.6 * 10-3 kg 
C)  1.4 *1014 kg 
D)  1.1 *1010 kg 
E)  120 kg 
A)  1.6 kg 
B)  1.6 * 10-3 kg 
C)  1.4 *1014 kg 
D)  1.1 *1010 kg 
E)  120 kg

Question 7

A particle of mass M moving at speed V << c has approximately what total energy?

Accepted Answer

A)  Mc2  
B)  MV2/2 
C)  cMV 
D)  Mc2/2 
E)  cMV/2 
A)  Mc2  
B)  MV2/2 
C)  cMV 
D)  Mc2/2 
E)  cMV/2

Question 8

Use the following scenario for the next question.
A 26-year-old biologist makes a trip to study alien life forms in a distant planet 10 light-years away. The round trip including a stay of 1 year in the distance planet takes 21.5 years according to the clock on earth. The biologist's son is 3-year-old when he left. Assume that the planet is not moving with respect to Earth, and the speed is the same for both outbound and inbound part of the journey.
-What is the difference in age between the mother and son after she returns back to Earth?

Accepted Answer

A)  7.0 years 
B)  16.8 years 
C)  23.0 years 
D)  30.0 years 
E)  37.0 years 
A)  7.0 years 
B)  16.8 years 
C)  23.0 years 
D)  30.0 years 
E)  37.0 years

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?

Accepted Answer

A)  5.7 *107 m/s 
B)  9.5 * 107 m/s 
C)  1.3 * 108 m/s 
D)  2.4 *108 m/s 
E)  2.7 * 108 m/s 
A)  5.7 *107 m/s 
B)  9.5 * 107 m/s 
C)  1.3 * 108 m/s 
D)  2.4 *108 m/s 
E)  2.7 * 108 m/s

Question 10

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.

Accepted Answer

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. 
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.

Question 11

At rest, pions have a proper lifetime of 26 ns. What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

Accepted Answer

A)  0.96c 
B)  0.84c 
C)  0.70c 
D)  0.41c 
E)  0.91c 
A)  0.96c 
B)  0.84c 
C)  0.70c 
D)  0.41c 
E)  0.91c

Question 12

Castor and Pollux, identical twins, get into their individual spaceships and blast off simultaneously. Castor's is the faster ship, both return to Earth simultaneously. Which of the following statements is true?

Accepted Answer

A)  Castor is older only if he traveled in the same direction as Pollux. 
B)  Castor is older only if he traveled in the opposite direction to Pollux. 
C)  Pollux is older only if he traveled in the same direction as Castor. 
D)  Pollux is older only if he traveled in the opposite direction to Castor. 
E)  Pollux is older. 
A)  Castor is older only if he traveled in the same direction as Pollux. 
B)  Castor is older only if he traveled in the opposite direction to Pollux. 
C)  Pollux is older only if he traveled in the same direction as Castor. 
D)  Pollux is older only if he traveled in the opposite direction to Castor. 
E)  Pollux is older.

Question 13

A clock has a period of exactly 1 second when at rest. If you were to measure a period of 1.5 seconds for the same clock, how fast is it moving relative to you as a percentage of the speed of light?

Accepted Answer

A)  44% 
B)  31% 
C)  67% 
D)  75% 
E)  87% 
A)  44% 
B)  31% 
C)  67% 
D)  75% 
E)  87%

Question 14

The expression relating the bending of the path of a relativistic, charged particle in a magnetic field to the particle's momentum is

Accepted Answer

A)  p2 = 2mB 
B)  p = qBr 
C)  E2 = (pc)2 + E02 
D)  p = q2B2r2/2m 
E)    
A)  p2 = 2mB 
B)  p = qBr 
C)  E2 = (pc)2 + E02 
D)  p = q2B2r2/2m 
E)

Question 15

The linear momentum (p) times the speed of light (c) of an electron traveling at 0.98c is

Accepted Answer

A)  0.495 MeV 
B)  0.511 MeV 
C)  1.12 MeV 
D)  2.5 MeV 
E)  938 MeV 
A)  0.495 MeV 
B)  0.511 MeV 
C)  1.12 MeV 
D)  2.5 MeV 
E)  938 MeV

Question 16

The mass of an electron traveling at 0.8c is how many times as great as its rest mass?

Accepted Answer

A)  0.60 
B)  0.78 
C)  0.80 
D)  1.28 
E)  1.67 
A)  0.60 
B)  0.78 
C)  0.80 
D)  1.28 
E)  1.67

Question 17

In the twenty-second century, a hyperfast New York to Los Angeles train roars through St. Louis without stopping at a speed of 0.80c. The front of the train arrives at the St. Louis station at precisely 12:00 noon according to all the clocks on the train (which are all synchronized in the train's frame), and the passengers are called to lunch in the dining car. An observer on the station platform manages to catch a glimpse of a clock at the front of the train that reads exactly 12:00 noon. What is the time at this instant at the rear of the train, according to the observer on the platform, if the train is 500 m long in its rest frame?

Accepted Answer

A)  1.35 $\mu$s past noon 
B)  1.35 $\mu$s before noon 
C)  noon exactly 
D)  1.35 ms past noon 
E)  1.35 ms before noon 
A)  1.35 $\mu$s past noon 
B)  1.35 $\mu$s before noon 
C)  noon exactly 
D)  1.35 ms past noon 
E)  1.35 ms before noon

Question 18

A star system is 100 light-years away. If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

Accepted Answer

A)  4.1 
B)  17 
C)  1.0 
D)  1.3 
E)  2.4 
A)  4.1 
B)  17 
C)  1.0 
D)  1.3 
E)  2.4

Question 19

The correct expression relating the energy E of a particle to its rest mass m0, its momentum p, and the speed of light c, is

Accepted Answer

A)  E2 = p2c2 + m0c2  
B)  E2 = p2c2 + (m0c)2  
C)  E2 = p2c + (m0c2)2  
D)  E2 = pc2 + (m0c2)2  
E)  E2 = p2c2 + (m0c2)2  
A)  E2 = p2c2 + m0c2  
B)  E2 = p2c2 + (m0c)2  
C)  E2 = p2c + (m0c2)2  
D)  E2 = pc2 + (m0c2)2  
E)  E2 = p2c2 + (m0c2)2

Question 20

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

Accepted Answer

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. 
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.

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 * 10⁸ m/s says the particle lived

Einstein's Second Postulate states that nothing can travel faster than the speed of light. The kinetic energy of a particle of rest mass m

The Sun radiates electromagnetic energy at the rate of 3.92 * 10²⁶ W. What is the change in the Sun's mass during each second that it is radiating energy?

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c. An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min). The time between beats according to a sympathetic astronaut aboard Klara is

The energy released by the nuclear bomb that destroyed Hiroshima was equivalent to 12.4 kilotons of TNT. This is equivalent to 9.0 * 10²⁶ MeV. The mass that was converted into energy in this explosion was

A particle of mass M moving at speed V << c has approximately what total energy?

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

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.

At rest, pions have a proper lifetime of 26 ns. What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

Castor and Pollux, identical twins, get into their individual spaceships and blast off simultaneously. Castor's is the faster ship, both return to Earth simultaneously. Which of the following statements is true?

A clock has a period of exactly 1 second when at rest. If you were to measure a period of 1.5 seconds for the same clock, how fast is it moving relative to you as a percentage of the speed of light?

The expression relating the bending of the path of a relativistic, charged particle in a magnetic field to the particle's momentum is

The linear momentum (p) times the speed of light (c) of an electron traveling at 0.98c is

The mass of an electron traveling at 0.8c is how many times as great as its rest mass?

A star system is 100 light-years away. If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

The correct expression relating the energy E of a particle to its rest mass m₀, its momentum p, and the speed of light c, is

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

The Electric Field I: Discrete Charge Distributions

The Electric Field II: Continuous Charge Distributions

Electric Potential

Capacitance

Electric Current and Direct-Current Circuits

The Magnetic Field

Sources of the Magnetic Field

Magnetic Induction

Alternating-Current Circuits

Maxwells Equations and Electromagnetic Waves

Properties of Light

Optical Images

Interference and Diffraction

Wave Particle Duality and Quantum Physics

Applications of the Schrodinger Equation

Atoms

Molecules

Solids and the Theory of Conduction

Nuclear Physics

Elementary Particles and the Beginning of the Universe

Filters

Exam 19: Relativity

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 * 108 m/s says the particle lived

Einstein's Second Postulate states that nothing can travel faster than the speed of light. The kinetic energy of a particle of rest mass m

The Sun radiates electromagnetic energy at the rate of 3.92 * 1026 W. What is the change in the Sun's mass during each second that it is radiating energy?

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c. An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min). The time between beats according to a sympathetic astronaut aboard Klara is

The energy released by the nuclear bomb that destroyed Hiroshima was equivalent to 12.4 kilotons of TNT. This is equivalent to 9.0 * 1026 MeV. The mass that was converted into energy in this explosion was

A particle of mass M moving at speed V << c has approximately what total energy?

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

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.

At rest, pions have a proper lifetime of 26 ns. What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

Castor and Pollux, identical twins, get into their individual spaceships and blast off simultaneously. Castor's is the faster ship, both return to Earth simultaneously. Which of the following statements is true?

A clock has a period of exactly 1 second when at rest. If you were to measure a period of 1.5 seconds for the same clock, how fast is it moving relative to you as a percentage of the speed of light?

The expression relating the bending of the path of a relativistic, charged particle in a magnetic field to the particle's momentum is

The linear momentum (p) times the speed of light (c) of an electron traveling at 0.98c is

The mass of an electron traveling at 0.8c is how many times as great as its rest mass?

A star system is 100 light-years away. If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

The correct expression relating the energy E of a particle to its rest mass m0, its momentum p, and the speed of light c, is

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

The Electric Field I: Discrete Charge Distributions

The Electric Field II: Continuous Charge Distributions

Electric Potential

Capacitance

Electric Current and Direct-Current Circuits

The Magnetic Field

Sources of the Magnetic Field

Magnetic Induction

Alternating-Current Circuits

Maxwells Equations and Electromagnetic Waves

Properties of Light

Optical Images

Interference and Diffraction

Wave Particle Duality and Quantum Physics

Applications of the Schrodinger Equation

Atoms

Molecules

Solids and the Theory of Conduction

Nuclear Physics

Elementary Particles and the Beginning of the Universe

Filters

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 * 10⁸ m/s says the particle lived

The Sun radiates electromagnetic energy at the rate of 3.92 * 10²⁶ W. What is the change in the Sun's mass during each second that it is radiating energy?

The energy released by the nuclear bomb that destroyed Hiroshima was equivalent to 12.4 kilotons of TNT. This is equivalent to 9.0 * 10²⁶ MeV. The mass that was converted into energy in this explosion was

The correct expression relating the energy E of a particle to its rest mass m₀, its momentum p, and the speed of light c, is