Deck 26: Relativity

Question 1

A tuning fork has a frequency of 300 Hz and hence a period of 3.33 × 10−³ s.If the tuning fork is in an inertial frame of reference moving by the observer at speed of 0.620 c,what is the frequency of the fork as measured by the observer? (Assume that measurements are strictly by optical means and that the speed of sound waves in air is not pertinent here).

A) 235 Hz
B) 382 Hz
C) 185 Hz
D) 185 Hz.
E) ​487 Hz

Answer 1

235 Hz

Question 2

The speed of light is equal to:

A) 5.28 × 10⁷ miles per hour.
B) one meter per nanosecond.
C) one light-year per year.
D) none of the above.

Answer 2

one light-year per year.

Question 3

According to the special theory of relativity,which of the following happens to the length of an object,measured in the dimension parallel to the motion of its inertial frame of reference,as the velocity of this frame increases with respect to a stationary observer?

A) length increases
B) length decreases
C) length remains constant
D) length vanishes to zero when velocity equals half speed of light

Answer 3

length decreases

Question 4

The Michelson-Morley experiment was designed to make use of ________ to find the motion of the Earth relative to the luminiferous ether.

A) sound waves
B) interference fringes
C) electromagnetic wind
D) none of the above

Question 5

The period of a pendulum is 1.5 s in a stationary inertial frame of reference.What is its period when measured by an observer moving at a speed of 0.75 c with respect to the inertial frame of reference?

A) 1.0 s
B) 3.4 s
C) 2.3 s
D) 3.0 s
E) ​0.8 s

Question 6

The period of an oscillating weight on a spring in an inertial frame of reference is 2.5 s.What would be its speed if it were to move by an observer who measures its period as 3.4 s? (c = 3.00 × 10⁸ m/s)

A) 1.5 × l0⁸ m/s
B) 2.0 × 10⁸ m/s
C) 2.8 × l0⁸ m/s
D) 6.8 × 10⁷ m/s
E) ​1.3 × 10⁸ m/s

Question 7

According to the special theory of relativity,if a 30-year old astronaut sent on a space mission is accelerated to speeds close to that of light,and then returns to earth after 20 years as measured on earth,what would be his biological age upon returning?

A) less than 50 years
B) 50 years
C) more than 50 years
D) exactly 100 years

Question 8

The observed relativistic length of a super rocket moving by the observer at 0.70 c will be what factor times that of the measured rocket length if it were at rest?

A) 0.55
B) 0.71
C) 0.51
D) 1.4
E) ​1.8

Question 9

Einstein's theory of relativity is based in part on which one of the following postulates?

A) Mass and energy are equivalent.
B) Space and time are absolutes.
C) Energy is conserved only in elastic collisions.
D) Speed of light in a vacuum is same for all observers regardless of source velocity.

Question 10

A mass is bouncing on the end of a spring with a period T when measured by a ground observer.What would the period of oscillation be (as measured by the same observer)if the mass and spring were moving past the ground observer at a speed of 0.9 c?

A) 5.3 T
B) 0.40 T
C) 3.2 T
D) 2.3 T
E) ​1.1 T

Question 11

Doubling the momentum of:

A) a particle doubles its relativistic total energy.
B) a particle quadruples its relativistic total energy.
C) a photon doubles its relativistic total energy.
D) a photon quadruples its relativistic total energy.

Question 12

The relativistic effect of time dilation has been verified by which of the following?

A) the discovery of black holes
B) muon experiments
C) twin experiments
D) red shift in distant galaxies

Question 13

I am stationary in a reference system but if my reference system is not an inertial reference system,then,relative to me,a system that is an inertial reference system must:

A) remain at rest.
B) move with constant velocity.
C) be accelerating.
D) be none of the above.

Question 14

A space probe has an 15.6-m length when measured at rest.What length does an observer at rest measure when the probe is going by at a speed of 0.740 c?

A) 23.2 m
B) 10.5 m
C) 8.0 m
D) 11.5 m
E) ​21.1 m

Question 15

According to the special theory of relativity,which of the following happens to the size of the time interval between two events occurring in an inertial frame of reference as the frame's velocity with respect to the observer increases?

A) interval increases
B) interval decreases
C) interval remains constant
D) interval vanishes to zero when velocity equals half speed of light

Question 16

According to a postulate of Einstein,which of the following describes the nature of the laws of physics as one observes processes taking place in various inertial frames of reference?

A) Laws are same only in inertial frames with zero velocity.
B) Laws are same only in inertial frames moving at low velocities.
C) Laws are same only in inertial frames moving at near speed of light.
D) Laws are same in all inertial frames.

Question 17

The experiment that dispelled the idea that light travels in the ether is called the:

A) Michelson-Morley experiment.
B) Hafele and Keating experiment.
C) Fitzgerald-Kennedy experiment.
D) twin paradox.

Question 18

That the speed of light in a vacuum has the same value for all inertial frames is:

A) inconsistent with the results of the Michelson-Morley experiment.
B) consistent with the results of the Michelson-Morley experiment.
C) not related to the results of the Michelson-Morley experiment.
D) not true.

Question 19

Which characterizes the main result of the Michelson-Morley experiment?

A) verified the existence of ether
B) involved measuring the speed of sound from a moving source
C) detected no difference in the speed of light regardless of speed of the source relative to observer
D) was designed purposely to verify Einstein's theory of relativity

Question 20

The significant result of the Michelson-Morley experiment was that it found:

A) the ether moved with the sun.
B) the ether moved with the Earth.
C) the speed of the ether wind was greater than expected.
D) no effect.

Question 21

From a stationary position,I observe a moving boxcar,which has a mirror along the front wall,but it is open at the back of the boxcar.I send a flash of light from my flashlight and time the flash of light as it goes to the front of the boxcar and returns to the back of the boxcar.A passenger in the boxcar also times the round trip of the flash of light.Previously I had measured the time required for the round trip of a flash of light when the boxcar was stationary,and I call this the stationary time.Which two times are the same?

A) the time recorded on my watch and the previous stationary time
B) the time recorded on the passenger's watch and the previous stationary time
C) the time recorded on my watch and the time recorded on the passenger's watch
D) None of the times are the same.

Question 22

A meter stick moving in a direction parallel to its length appears to be only 43.6 cm long to an observer.What is the meter stick's speed relative to the observer? (c = 3.00 × 10⁸ m/s)

A) 2.25 × 10⁸ m/s
B) 1.69 × 10⁸ m/s
C) 2.70 × 10⁸ m/s
D) 1.31 × 10⁸ m/s
E) ​2.95 × 10⁸ m/s

Question 23

Muons at speed 0.9995 c are sent round and round a circular storage ring of radius 550 m.If a muon at rest decays into other particles after an average T =2.2 × 10−⁶ s,how many trips around the storage ring do we expect the 0.9995 c muons to make before they decay?

A) 1
B) 2
C) 12
D) 6
E) ​131

Question 24

A boxcar without a front or a back is moving toward the right.Two flashes of light move through the boxcar,one moving from back to front toward the right,the other moving from front to back toward the left.A passenger in the boxcar records how long it takes each flash of light to pass from one end of the boxcar to the other end.According to the passenger,which took longer?

A) the flash going from back to front
B) the flash going from front to back
C) They both took the same time.
D) It depends on whether the passenger is sitting at the front or the back of the boxcar.

Question 25

The total energy of a particle:

A) is not related to its relativistic momentum.
B) increases with increasing relativistic momentum.
C) decreases with increasing relativistic momentum.
D) is a constant.

Question 26

A proton with mass 1.67 × 10−²⁷ kg moves with a speed of 0.760 c in an accelerator.What is its relativistic momentum? (c = 3.00 × 10⁸ m/s)

A) 3.65E-19 kg⋅m/s
B) 7.90E-20 kg⋅m/s
C) 5.61E-19 kg⋅m/s
D) 2.37E-19 kg⋅m/s
E) ​4.80E-19 kg·m/s

Question 27

The short lifetime of muons created in the upper atmosphere of the Earth would not allow them to reach the surface of the Earth unless their lifetime increased by time dilation.From the reference system of the muons,the muons can reach the surface of the Earth because:

A) time dilation increases their velocity.
B) time dilation increases their energy.
C) length contraction decreases the distance to the Earth.
D) the relativistic speed of the Earth toward them is added to their velocity.

Question 28

If astronauts could travel at v = 0.95 c,we on Earth would say it takes (4.2/0.95)= 4.4 years to reach Alpha Centauri,4.2 lightyears away.The astronauts disagree.How much time passes on the astronaut's clocks?

A) 1.4 years
B) 14.1 years
C) 4.0 years
D) 1.3 years
E) ​0.4 years

Question 29

A muon formed high in the Earth's atmosphere travels at a speed 0.870 c for a distance of 4.00 km before it decays.What is the muon's lifetime as measured in its reference frame?

A) 3.1E-5 s
B) 7.6E-6 s
C) 1.5E-5 s
D) 5.1E-5 s
E) ​4.3E-5 s

Question 30

A rocket ship is 87.0 m in length when measured before leaving the launching pad.What would its velocity be if a ground observer measured its length as 62.0 m while it is in flight? (c = 3.00 × 10⁸ m/s)

A) 1.61 × 10⁸ m/s
B) 2.14 × 10⁸ m/s
C) 1.48 × 10⁸ m/s
D) 2.10 × 10⁸ m/s
E) ​1.91 × 10⁸ m/s

Question 31

How fast would a rocket have to move past a ground observer if the latter were to observe a 9.4% length shrinkage in the rocket length? (c = 3.00 × 10⁸ m/s)

A) 2.98 × 10⁸ m/s
B) 2.72 × 10⁸ m/s
C) 1.27 × 10⁸ m/s
D) 0.420 × 10⁸ m/s
E) ​0.920 × 10⁸ m/s

Question 32

A spaceship of triangular shape,having a length three its width,is capable of relativistic speeds.How fast would it have to move so that to a stationary observer its length would equal its width?

A) 0.333 c
B) 0.816 c
C) 0.943 c
D) ​0.650 c
E) ​This is not possible.

Question 33

A muon formed high in Earth's atmosphere travels at a speed 0.960 c for a distance (as we see it)of 4500 m before it decays.How far does the muon travel as measured in its frame?

A) 2520 m
B) 16,100 m
C) 4320 m
D) 1260 m
E) ​4500 m

Question 34

At what speed would a clock have to be moving in order to run at a rate that is one-fourth the rate of a clock at rest?

A) 0.87 c
B) 0.75 c
C) 0.97 c
D) 0.50 c
E) ​0.26 c

Question 35

At what speed is the momentum of an object five times that found classically?

A) 0.894 c
B) 0.960 c
C) 0.980 c
D) 0.800 c
E) ​0.999 c

Question 36

As the speed of an object increases,its relativistic momentum:

A) stays the same as its classical momentum.
B) increases more than its classical momentum.
C) increases less than it classical momentum.
D) does not change since momentum is a conserved quantity.

Question 37

Including relativistic effects,doubling the speed of a object:

A) doubles its momentum.
B) more than doubles its momentum.
C) less than doubles its momentum.
D) has no effect on its momentum.

Question 38

In a test of equipment the following procedure is carried out.Spacecraft №1 is traveling at 0.75 c and fires a laser pulse in the forward direction at Spacecraft №2,which is testing its device that measures the speed of laser pulses as they pass by the spacecraft.Spacecraft №2 is traveling at 0.95 c in a direction away from Spacecraft №1.The device is working properly,and the speed of the pulse as it passes is successfully measured.What is the speed of the laser pulse measured in this case?

A) 0.80 c
B) 0.70 c
C) c
D) This is a question that cannot be answered without knowing in which reference frames the speeds given in the problem.If you agree,then this is the answer that you should choose.

Question 39

From a stationary position,I observe a moving boxcar,which has a mirror along the front wall,but it is open at the back of the boxcar.I send a flash of light from my flashlight and time the flash of light as it goes to the front of the boxcar and returns to the back of the boxcar.A passenger in the boxcar also times the round trip of the flash of light.Compare the times recorded on our watches.

A) The time recorded on his watch is longer.
B) The time recorded on the two watches is the same.
C) The time recorded on his watch is shorter.
D) The answer depends on the reference system you are in.

Question 40

An astronaut at rest has a heart rate of 68 beats/min.What will her heart rate be as measured by an earth observer when the astronaut's spaceship goes by the earth at a speed of 0.76 c?

A) 105 beats/min
B) 52 beats/min
C) 33 beats/min
D) 139 beats/min
E) ​44 beats/min

Question 41

An unknown particle in an accelerator moving at a speed of 1.50 × 10⁸ m/s has a measured total energy of 3.30 × 10−⁹ J.What is its mass? (c = 3.00 × 10⁸ m/s)

A) 4.23E-26 kg
B) 9.17E-27 kg
C) 7.78E-26 kg
D) 3.18E-26 kg
E) ​3.67E-26 kg

Question 42

If the mass of a proton is 1.67 × 10−²⁷ kg,what is the rest energy of the proton? (c = 3.00 × 10⁸ m/s and 1 eV = 1.6 × 10−¹⁹ J)

A) 1.2 × 10⁸ eV
B) 3.7 × 10⁸ eV
C) 4.1 × 10⁸ eV
D) 9.4 × 10⁸ eV

Question 43

When a one-megaton nuclear bomb is exploded,approximately 4.0 × 10¹⁵ J of energy is released.How much mass would this represent in a mass-to-energy conversion? (c = 3.00 × 10⁸ m/s)

A) 1.333 × 10⁶ kg
B) 0.044 kg
C) 0.444 kg
D) 3.600 kg
E) ​4.0 × 10³ kg

Question 44

A spaceship,which has length 35 m and width 16 m when at rest,is moving in a direction along its length at a speed where its length contraction results in a 28-m length measured by a stationary observer.What would the measured width be in this case?

A) between 18 and 20 m
B) 16 m
C) 13 m
D) less than 13 m
E) ​20 m

Question 45

The gravitational field is equivalent to:

A) the inertial mass.
B) an accelerated frame of reference.
C) an event horizon.
D) a clock running slowly.

Question 46

A proton with mass 1.67 × 10−²⁷ kg moves with a speed of 0.560 c in an accelerator.What is its kinetic energy? (c = 3.00 × 10⁸ m/s)

A) 1.50E-10 J
B) 1.81E-10 J
C) 3.11E-11 J
D) 1.03E-10 J
E) ​4.71E-11 J

Question 47

Through what potential difference would an electron initially at rest need to be accelerated to have its total energy be five times its rest energy? (m_e = 9.11 × 10^-31 kg,c = 3.00 × 10⁸ m/s,and q_e = 1.6 × 10−¹⁹ C)

A) 1.6E-19 V
B) 2.6E+6 V
C) 2.0E+6 V
D) 210 V
E) ​6.8E-3 V

Question 48

A spaceship is moving away from an observer at relativistic speed.Its length at rest is 100 m,but the observer measures its length as 60 m.A time interval of 84 s on the spaceship would be measured by the observer to be which of the following?

A) 50.4 s
B) 30.2 s
C) 134 s
D) 140 s
E) ​84 s

Question 49

At what speed must an object be moving in order that it has a kinetic energy 2.6 times its rest energy? (c = 3.00 × 10⁸ m/s)

A) 2.77 × 10⁸ m/s
B) 2.17 × 10⁸ m/s
C) 2.88 × 10⁸ m/s
D) 1.15 × 10⁸ m/s
E) ​2.55 × 10⁸ m/s

Question 50

When one compares the relativistic kinetic energy to the classically calculated kinetic energy for a moving object,at which of the speeds listed below does the classical calculation give a greater value than the relativistic calculation?

A) 0.2 c
B) 0.5 c
C) 0.707 c
D) None of the above values will give such a result.

Question 51

Relativity dealing with gravitation is known as:

A) inertial relativity.
B) gravitational relativity.
C) Galilean relativity.
D) general relativity.

Question 52

A satellite is powered by a small nuclear generator that puts out 10 W.How much matter is converted into energy over the 20 year life span of the generator?

A) 70 µg
B) 70 g
C) 7 g
D) 7 kg
E) ​4 mg

Question 53

If the total energy of an electron in an accelerator is three times its rest energy,what is its speed? (c = 3.00 × 10⁸ m/s)

A) 2.00 × 10⁸ m/s
B) 1.30 × 10⁸ m/s
C) 1.41 × 10⁸ m/s
D) 2.98 × 10⁸ m/s
E) ​2.83 × 10⁸ m/s

Question 54

What is the relativistic kinetic energy of an electron moving at a speed of 2.30 × 10⁸ m/s? (electron mass is 9.11 × 10−³¹ kg and c = 3.00 × 10⁸ m/s)

A) 4.57E-14 J
B) 1.28E-13 J
C) 5.26E-14 J
D) 3.38E-14 J
E) ​8.20E-14 J

Question 55

A lump of uranium has a mass of 2.0 kg,and begins at rest.Half of the lump's mass is going to be totally converted into kinetic energy of the other half.After this is done,how fast is the remaining half going?

A) 0.60 c
B) 0.80 c
C) 0.87 c
D) 1.0 c

Question 56

A nuclear reaction,which gives off a total of 1.2 × 10¹⁷ J of energy,expends how much mass in the process? (c = 3.00 × 10⁸ m/s)

A) 0.1 kg
B) 1.3 kg
C) 4.0 kg
D) 13.3 kg
E) ​7.5 kg

Question 57

In an x-ray tube,high-speed electrons are slammed into a lead target,giving off x-rays.If the electrons are accelerated from rest through a potential difference of 160 000 volts,what speed do they have when they strike the target? (q_e = 1.6 × 10−¹⁹ C,m_e = 9.11 × 10−³¹ kg,and c = 3.00 × 10⁸ m/s)

A) 0.79 c
B) 0.65 c
C) 0.83 c
D) 0.49 c
E) ​0.48 c

Question 58

The mass of a proton at rest is m_. If the proton is moving so fast that its total energy is three times its rest energy,then what is the kinetic energy of the proton?

A) mc²
B) 2mc²
C) 3mc²
D) 4mc²

Question 59

What is the total energy of a proton moving at a speed of 2.4 × 10⁸ m/s? (proton mass is 1.67 × 10−²⁷ kg and c = 3.00 × 10⁸ m/s)

A) 1.91E-10 J
B) 1.77E-10 J
C) 2.51E-10 J
D) 2.44E-10 J
E) ​9.02E-11 J

Question 60

If a proton with mass 1.67 × 10−²⁷ kg moves in an accelerator such that its total energy is three times its rest energy,what is its speed? (c = 3.00 × 10⁸ m/s)

A) 2.83 × 10⁸ m/s
B) 2.45 × 10⁸ m/s
C) 2.00 × 10⁸ m/s
D) 1.00 × 10⁸ m/s
E) ​1.54 × 10⁸ m/s

Question 61

Which form of relativity applies for observers who are accelerating?

A) Special relativity applies.
B) General relativity applies.
C) Both special relativity and general relativity apply.
D) Neither applies since the observer must be in an inertial frame to use either one.

Question 62

If the nonzero momentum of a particle with mass is doubled,what happens to its total energy?

A) It also doubles.
B) It increases,more than doubling.
C) It stays the same since total energy is a constant for a given particle.
D) It increases,but less than doubling.