Question 1

Pi mesons at rest have a half-life of T. If a beam of pi mesons is traveling at a speed of v = $\beta$c, the distance in which the intensity of the beam is halved is:

Accepted Answer

A)  c$\beta$T(1 - $\beta$2)-1/2 
B)  c$\beta$T[(1 + $\beta$)/(1 - $\beta$)]1/2 
C)  $\beta$vT 
D)  (1 - $\beta$2)1/2vT 
E)  none of the above 
A)  c$\beta$T(1 - $\beta$2)-1/2 
B)  c$\beta$T[(1 + $\beta$)/(1 - $\beta$)]1/2 
C)  $\beta$vT 
D)  (1 - $\beta$2)1/2vT 
E)  none of the above

Question 2

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 3

If the mass of a particle is zero its speed must be:

Accepted Answer

A)  c 
B)  infinite 
C)  0 
D)  any speed less than c 
E)  any speed greater than c 
A)  c 
B)  infinite 
C)  0 
D)  any speed less than c 
E)  any speed greater than c

Question 4

According to the theory of relativity:

Accepted Answer

A)  moving clocks run fast 
B)  energy is not conserved in high speed collisions 
C)  the speed of light must be measured relative to the ether 
D)  momentum is not conserved in high speed collisions 
E)  none of the above 
A)  moving clocks run fast 
B)  energy is not conserved in high speed collisions 
C)  the speed of light must be measured relative to the ether 
D)  momentum is not conserved in high speed collisions 
E)  none of the above

Question 5

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)  0.8c 
E)  c 
A)  0.33c 
B)  0.50c 
C)  0.71c 
D)  0.8c 
E)  c

Question 6

According to the theory of relativity:

Accepted Answer

A)  all forms of energy have mass-like properties 
B)  moving particles lose mass 
C)  momentum is not conserved in high speed collisions 
D)  a rod moving rapidly sideways is shorter along its length 
E)  a rod moving rapidly sideways is longer along its length 
A)  all forms of energy have mass-like properties 
B)  moving particles lose mass 
C)  momentum is not conserved in high speed collisions 
D)  a rod moving rapidly sideways is shorter along its length 
E)  a rod moving rapidly sideways is longer along its length

Question 7

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

Question 8

A rocket traveling with constant velocity makes a 8.4 *1015 m trip in 1 year. The proper time in years between events which mark the beginning and end of the trip is:

Accepted Answer

A)  0.21 
B)  0.46 
C)  1.0 
D)  2.2 
E)  4.7 
A)  0.21 
B)  0.46 
C)  1.0 
D)  2.2 
E)  4.7

Question 9

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 10

Two flashes of light occur simultaneously at t = 0 in reference frame S, one at x = 0 and the other at x = 600 m. They are observed in reference frame S', which is moving at 0.95c in the positive x direction. The origins of the two frames coincide at t = 0 and the clocks of S' are zeroed when the origins coincide. In S' the coordinate where the leading edges of the two light flashes meet and the time when they meet are:

Accepted Answer

A)  300 m, 1.0 $\mu$s 
B)  15 m, 0.050 $\mu$s 
C)  585 m, 1.95 $\mu$s 
D)  48 m, 0.16 $\mu$s 
E)  1900 m, 0.16 $\mu$s 
A)  300 m, 1.0 $\mu$s 
B)  15 m, 0.050 $\mu$s 
C)  585 m, 1.95 $\mu$s 
D)  48 m, 0.16 $\mu$s 
E)  1900 m, 0.16 $\mu$s

Question 11

The work that must be done to increase the speed of an electron (m = 9.11 * 10-31 kg) from 0.90c to 0.95c is:

Accepted Answer

A)  2.6 * 10-13 J 
B)  8.2 * 10-13 J 
C)  3.2 * 10-13 J 
D)  7.4 *10-14 J 
E)  3.8 * 10-15 J 
A)  2.6 * 10-13 J 
B)  8.2 * 10-13 J 
C)  3.2 * 10-13 J 
D)  7.4 *10-14 J 
E)  3.8 * 10-15 J

Question 12

The mass of a particle is m. In order for its total energy to be twice its rest energy, its momentum must be:

Accepted Answer

A)  mc/2 
B)    
C)  mc 
D)    
E)  2mc 
A)  mc/2 
B)    
C)  mc 
D)    
E)  2mc

Question 13

An electron is moving at 0.6c. If we calculate its kinetic energy using (1/2)mv2, we get a result which is:

Accepted Answer

A)  just right 
B)  just half enough 
C)  twice the correct value 
D)  about 1% too low 
E)  about 28% too low 
A)  just right 
B)  just half enough 
C)  twice the correct value 
D)  about 1% too low 
E)  about 28% too low

Question 14

Two electrons move in opposite directions at 0.70c as measured in the laboratory. The speed of one electron as measured from the other is:

Accepted Answer

A)  0.35c 
B)  0.70c 
C)  0.94c 
D)  1.00c 
E)  1.40c 
A)  0.35c 
B)  0.70c 
C)  0.94c 
D)  1.00c 
E)  1.40c

Question 15

A consequence 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 longer 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 run more slowly than when they are at rest 
B)  moving rods are longer 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

Question 16

Two events occur simultaneously on the x axis of reference frame S,one at x =+a and the other at x = +a. According to an observer moving in the positive x direction:

Accepted Answer

A)  the event at x = +a occurs first 
B)  the event x =+a occurs first 
C)  either event might occur first, depending on the value of a and the observer's speed 
D)  the events are simultaneous 
E)  none of the above 
A)  the event at x = +a occurs first 
B)  the event x =+a occurs first 
C)  either event might occur first, depending on the value of a and the observer's speed 
D)  the events are simultaneous 
E)  none of the above

Question 17

Light from some stars shows an apparent change in frequency because of:

Accepted Answer

A)  interference 
B)  refraction by layers of air 
C)  diffraction 
D)  reflection 
E)  relative motion 
A)  interference 
B)  refraction by layers of air 
C)  diffraction 
D)  reflection 
E)  relative motion

Question 18

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

Question 19

A certain automobile is 6 m long if at rest. If it is measured to be 4/5 as long, its speed is:

Accepted Answer

A)  0.1c 
B)  0.3c 
C)  0.6c 
D)  0.8c 
E)  > 0.95c 
A)  0.1c 
B)  0.3c 
C)  0.6c 
D)  0.8c 
E)  > 0.95c

Question 20

A consequence of Einstein's theory of relativity is:

Accepted Answer

A)  moving clocks run faster 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 appear the same to all observers moving with uniform velocity relative to each other 
E)  everything is relative 
A)  moving clocks run faster 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 appear the same to all observers moving with uniform velocity relative to each other 
E)  everything is relative

Exam 37: Relativity

Pi mesons at rest have a half-life of T. If a beam of pi mesons is traveling at a speed of v = β\betaβ c, the distance in which the intensity of the beam is halved 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 mass of a particle is zero its speed must be:

According to the theory of relativity:

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:

According to the theory of relativity:

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 rocket traveling with constant velocity makes a 8.4 *1015 m trip in 1 year. The proper time in years between events which mark the beginning and end of the trip 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:

The work that must be done to increase the speed of an electron (m = 9.11 * 10-31 kg) from 0.90c to 0.95c is:

The mass of a particle is m. In order for its total energy to be twice its rest energy, its momentum must be:

An electron is moving at 0.6c. If we calculate its kinetic energy using (1/2)mv2, we get a result which is:

Two electrons move in opposite directions at 0.70c as measured in the laboratory. The speed of one electron as measured from the other is:

A consequence of Einstein's theory of relativity is:

Two events occur simultaneously on the x axis of reference frame S,one at x =+a and the other at x = +a. According to an observer moving in the positive x direction:

Light from some stars shows an apparent change in frequency because of:

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

A certain automobile is 6 m long if at rest. If it is measured to be 4/5 as long, its speed is:

A consequence of Einstein's theory of relativity is:

Measurement

Motion Along a Straight Line

Vector

Motion in Two and Three Dimensions

Force and Motion I

Force and Motion II

Kinetic Energy and Work

Potential Energy and Conservation of Energy

Center of Mass and Linear Momentum

Rotation

Rolling, Torque, and Angular Momentum

Equilibrium and Elasticity

Gravitation

Fluids

Oscillations

Waves I

Waves II

Temperature, Heat, and the First Law of Thermodynamics

The Kinetic Theory of Gases

Entropy and the Second Law of Thermodynamics

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Gauss Law

Electric Potential

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Current and Resistance

Circuits

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Magnetic Fields Due to Currents

Induction and Inductance

Electromagnetic Oscillations and Alternating Current

Maxwells Equations; Magnetism of Matter

Electromagnetic Waves

Images

Interference

Diffraction

Photons and Matter Waves

More About Matter Waves

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Conduction of Electricity in Solids

Nuclear Physics

Energy From the Nucleus

Quarks, Leptons, and the Big Bang

Filters

Pi mesons at rest have a half-life of T. If a beam of pi mesons is traveling at a speed of v = $\beta$ c, the distance in which the intensity of the beam is halved is:

A rocket traveling with constant velocity makes a 8.4 *10¹⁵ m trip in 1 year. The proper time in years between events which mark the beginning and end of the trip is:

The work that must be done to increase the speed of an electron (m = 9.11 * 10^-³¹ kg) from 0.90c to 0.95c is:

An electron is moving at 0.6c. If we calculate its kinetic energy using (1/2)mv², we get a result which is: