Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Question 6

You observed that event A occurred before event B.Which of the following statements is false?

Accepted Answer

A) Another reference frame must exist in which event A precedes event B. 
B) A reference frame must exist in which event B precedes A. 
C) A reference frame could exist in which the events are simultaneous. 
D) A reference frame could not exist in which event B precedes event A. 
E) None of these statements is false.

Question 7

The Michelson-Morley experiment showed

Accepted Answer

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.

Question 8

If the ratio of the rest mass to the relativistic mass of an electron is 0.8,then the velocity of the electron must be

Accepted Answer

A) 0.2c 
B) 0.4c 
C) 0.6c 
D) 0.8c 
E) c

Question 9

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

Accepted Answer

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.

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.

Question 11

Alpha Centauri is not only the closest star system to us (it is actually a triple star system)but it also seems to be an excellent place to look for extra-terrestrial life.It is about 4.3 light-years away from Earth.If an astronaut claims her journey there and back only took 6.3 years,then how fast was she traveling? (Assume she made a fast turnaround once she arrived there!)

Accepted Answer

A) 0.65c 
B) 0.73c 
C) 0.86c 
D) 0.81c 
E) 0.54c

Question 12

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

Question 13

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c.An astronaut aboard Hari observes the length of Solange to be 30.5 m.The astronauts aboard Solange claim that the length of their spaceship is

Accepted Answer

A) 18.3 m 
B) 24.4 m 
C) 30.5 m 
D) 38.1 m 
E) 39.6 m

Question 14

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 particles moving toward them at 0.2c relative to Earth.One of the particles has a rest energy of 3.0 GeV and a momentum,as measured by the astronauts,of 4.0 GeV/c.Its kinetic energy is

Accepted Answer

A) 7.0 GeV 
B) 4.0 GeV 
C) 5.0 GeV 
D) 2.7 GeV 
E) 2.0 GeV

Question 15

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 $\times$ 10-8 s,then calculate how fast the beam is traveling.

Accepted Answer

A) 0.96c 
B) 0.92c 
C) 0.29c 
D) 0.98c 
E) 3.5c

Question 16

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m.If the Starcruiser is moving at 80% the speed of light,what would be its length if it was at rest relative to you?

Accepted Answer

A) 280 m 
B) 60 m 
C) 36 m 
D) 170 m 
E) 125 m

Question 17

Because the galaxies are moving away from us,the light they emit

Accepted Answer

A) is shifted toward the shorter,blue wavelengths. 
B) is shifted toward the longer,red wavelengths. 
C) is of the same wavelength it would be if they were at rest relative to Earth. 
D) arrives with increased intensity. 
E) None of these is correct.

Question 18

How fast does an electron have to travel to have the same mass as a proton at rest?

Accepted Answer

A) 0.9985c 
B) 0.999985c 
C) 0.9999985c 
D) 0.99999985c 
E) 0.9999999985c

Question 19

A radioactive atom is traveling through the laboratory at a speed of 0.2c when it undergoes beta decay.The emitted electron moves in the same direction as the atom and has a speed of 0.9c relative to the atom.The speed of the electron,as seen by an observer in the laboratory,is

Accepted Answer

A) 1.10c 
B) 1.07c 
C) c 
D) 0.93c 
E) 0.70c

Question 20

If one gram of matter could be completely converted into energy,the yield would be

Accepted Answer

A) 0.51 MeV 
B) 931 MeV 
C) 3 F$\times$ 1013 J 
D) 9 $\times$ 1013 J 
E) 9 $\times$ 1016 J

Exam 39: Relativity

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?

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

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

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.)

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

You observed that event A occurred before event B.Which of the following statements is false?

The Michelson-Morley experiment showed

If the ratio of the rest mass to the relativistic mass of an electron is 0.8,then the velocity of the electron must be

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

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.

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

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c.An astronaut aboard Hari observes the length of Solange to be 30.5 m.The astronauts aboard Solange claim that the length of their spaceship is

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 $\times$ 10^-8 s,then calculate how fast the beam is traveling.

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m.If the Starcruiser is moving at 80% the speed of light,what would be its length if it was at rest relative to you?

Because the galaxies are moving away from us,the light they emit

How fast does an electron have to travel to have the same mass as a proton at rest?

A radioactive atom is traveling through the laboratory at a speed of 0.2c when it undergoes beta decay.The emitted electron moves in the same direction as the atom and has a speed of 0.9c relative to the atom.The speed of the electron,as seen by an observer in the laboratory,is

If one gram of matter could be completely converted into energy,the yield would be

Exam 39: Relativity

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?

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

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

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.)

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

You observed that event A occurred before event B.Which of the following statements is false?

The Michelson-Morley experiment showed

If the ratio of the rest mass to the relativistic mass of an electron is 0.8,then the velocity of the electron must be

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

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.

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

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c.An astronaut aboard Hari observes the length of Solange to be 30.5 m.The astronauts aboard Solange claim that the length of their spaceship is

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 ×\times× 10-8 s,then calculate how fast the beam is traveling.

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m.If the Starcruiser is moving at 80% the speed of light,what would be its length if it was at rest relative to you?

Because the galaxies are moving away from us,the light they emit

How fast does an electron have to travel to have the same mass as a proton at rest?

A radioactive atom is traveling through the laboratory at a speed of 0.2c when it undergoes beta decay.The emitted electron moves in the same direction as the atom and has a speed of 0.9c relative to the atom.The speed of the electron,as seen by an observer in the laboratory,is

If one gram of matter could be completely converted into energy,the yield would be

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

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 $\times$ 10^-8 s,then calculate how fast the beam is traveling.