Question 1

The velocity of an electron is changed from c/2 in the -x direction to c/2 in the +x direction. As a result, its kinetic energy changes by:

Accepted Answer

A)  mc2 
B)  0.5mc2 
C)    
D)  2mc2 
E)  zero 
A)  mc2 
B)  0.5mc2 
C)    
D)  2mc2 
E)  zero

Question 2

Light from a stationary spaceship is observed, then the spaceship moves directly away from the observer at high speed. As a result, the light seen by the observer has:

Accepted Answer

A)  a higher frequency and a longer wavelength than before 
B)  a lower frequency and a shorter wavelength than before 
C)  a higher frequency and a shorter wavelength than before 
D)  a lower frequency and a longer wavelength than before 
E)  the same frequency and wavelength as before 
A)  a higher frequency and a longer wavelength than before 
B)  a lower frequency and a shorter wavelength than before 
C)  a higher frequency and a shorter wavelength than before 
D)  a lower frequency and a longer wavelength than before 
E)  the same frequency and wavelength as before

Question 3

The length of a meter stick moving at 0.95c in the direction of its length is measured by simultaneously marking its ends on a stationary axis. As measured by clocks moving with the stick, the time interval between the making of the back mark and the making of the front mark is:

Accepted Answer

A)  0 
B)  3.1 * 10-10 s 
C)  1.0 * 10-9 s 
D)  3.2 *10-9 s 
E)  1.0 *10-8 s 
A)  0 
B)  3.1 * 10-10 s 
C)  1.0 * 10-9 s 
D)  3.2 *10-9 s 
E)  1.0 *10-8 s

Question 4

As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9 * 10-8 s later a mark is made on the axis at the back end. The marks are found to be 100 m apart. The rest length of the rocket is:

Accepted Answer

A)  31 m 
B)  78 m 
C)  100 m 
D)  240 m 
E)  320 m 
A)  31 m 
B)  78 m 
C)  100 m 
D)  240 m 
E)  320 m

Question 5

Frame S' moves in the positive x direction at 0.6c with respect to frame S. A particle moves in the positive x direction at 0.4c as measured by an observer in S'. The speed of the particle as measured by an observer in S is:

Accepted Answer

A)  c/5 
B)  5c/19 
C)  8c/25 
D)  25c/31 
E)  c 
A)  c/5 
B)  5c/19 
C)  8c/25 
D)  25c/31 
E)  c

Question 6

Relative to reference frame 1, reference frame 2 moves with speed v in the negative x direction. When the origins of the two frames coincide the clocks in both frames are set to zero. An event occurs at coordinate x1 and time t1 as measured in reference frame 1 and at coordinate x2 and time t2 as measured in frame 2. If   , then the coordinates and times of the event are related by:

Accepted Answer

A)  x2 = $\gamma$[x1 - vt1] and t2 = $\gamma$[t1 - vx1 / c2] 
B)  x2 = $\gamma$[x1 - vt1] and t2 = $\gamma$[t1 + vx1 / c2] 
C)  x2 = $\gamma$[x1 + vt1] and t2 = $\gamma$[t1 - vx1 / c2] 
D)  x2 = $\gamma$[x1 + vt1] and t2 = $\gamma$[t1 + vx1 / c2] 
E)  none of the above are correct 
A)  x2 = $\gamma$[x1 - vt1] and t2 = $\gamma$[t1 - vx1 / c2] 
B)  x2 = $\gamma$[x1 - vt1] and t2 = $\gamma$[t1 + vx1 / c2] 
C)  x2 = $\gamma$[x1 + vt1] and t2 = $\gamma$[t1 - vx1 / c2] 
D)  x2 = $\gamma$[x1 + vt1] and t2 = $\gamma$[t1 + vx1 / c2] 
E)  none of the above are correct

Question 7

Two events occur 100 m apart with an intervening time interval of 0.60$\mu$s. The speed of a reference frame in which they occur at the same coordinate is:

Accepted Answer

A)  0 
B)  0.25c 
C)  0.56c 
D)  1.1c 
E)  1.8c 
A)  0 
B)  0.25c 
C)  0.56c 
D)  1.1c 
E)  1.8c

Question 8

While emitting light of proper frequency f0, a source moves to the right with speed c/4 relative to reference frame S. A detector, to the left of the source, measures the frequency to be f, which is greater than f0. This means:

Accepted Answer

A)  the detector is moving to the right with a speed that is greater than c/4 relative to S 
B)  the detector is moving to the right with a speed that is less than c/4 relative to S 
C)  the detector is moving to the left with a speed that is greater than c/4 relative to S 
D)  the detector is moving to the left with a speed that is less than c/4 relative to S 
E)  the detector is not moving 
A)  the detector is moving to the right with a speed that is greater than c/4 relative to S 
B)  the detector is moving to the right with a speed that is less than c/4 relative to S 
C)  the detector is moving to the left with a speed that is greater than c/4 relative to S 
D)  the detector is moving to the left with a speed that is less than c/4 relative to S 
E)  the detector is not moving

Question 9

Visible light, with a frequency of 6.0 *1014 Hz, is reflected from a spaceship moving directly away at a speed of 0.90c. The frequency of the reflected waves observed at the source is:

Accepted Answer

A)  3.2 *1013 Hz 
B)  1.4 * 1014 Hz 
C)  6.0 * 1014 Hz 
D)  2.6 * 1015 Hz 
E)  1.1 *1016 Hz 
A)  3.2 *1013 Hz 
B)  1.4 * 1014 Hz 
C)  6.0 * 1014 Hz 
D)  2.6 * 1015 Hz 
E)  1.1 *1016 Hz

Question 10

If the kinetic energy of a free particle is much less 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 11

A basic postulate 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 shorter than when they are at rest 
C)  light has both wave and particle properties 
D)  the laws of physics must be the same for 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 shorter than when they are at rest 
C)  light has both wave and particle properties 
D)  the laws of physics must be the same for observers moving with uniform velocity relative to each other 
E)  everything is relative

Question 12

A meson when at rest decays 2 $\mu$s after it is created. If moving in the laboratory at 0.99c, its lifetime according to laboratory clocks would be:

Accepted Answer

A)  the same 
B)  0.28 s 
C)  14 $\mu$s 
D)  4.6 s 
E)  none of these 
A)  the same 
B)  0.28 s 
C)  14 $\mu$s 
D)  4.6 s 
E)  none of these

Question 13

Two events occur 100 m apart with an intervening time interval of 0.37 $\mu$s. The speed of a clock that measures the proper time between the events is:

Accepted Answer

A)  0 
B)  0.45c 
C)  0.56c 
D)  0.90c 
E)  1.8c 
A)  0 
B)  0.45c 
C)  0.56c 
D)  0.90c 
E)  1.8c

Question 14

Two events occur simultaneously at separated points on the y axis of reference frame S. According to an observer moving in the positive x direction:

Accepted Answer

A)  the event with the greater y coordinate occurs first 
B)  the event with the greater y coordinate occurs last 
C)  either event might occur first, depending on the observer's speed 
D)  the events are simultaneous 
E)  none of the above 
A)  the event with the greater y coordinate occurs first 
B)  the event with the greater y coordinate occurs last 
C)  either event might occur first, depending on the observer's speed 
D)  the events are simultaneous 
E)  none of the above

Question 15

A particle with zero mass and energy E carries momentum:

Accepted Answer

A)  Ec 
B)  Ec2 
C)    
D)  E/c 
E)  E/c2 
A)  Ec 
B)  Ec2 
C)    
D)  E/c 
E)  E/c2

Question 16

A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c away from 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 17

Two independent events occur 100 m apart with an intervening time interval of 0.42 $\mu$s. The proper time in $\mu$s between the events is:

Accepted Answer

A)  0 
B)  0.16 
C)  0.26 
D)  0.42 
E)  0.69 
A)  0 
B)  0.16 
C)  0.26 
D)  0.42 
E)  0.69

Question 18

If the kinetic energy of a particle is equal to its rest energy then its speed must be:

Accepted Answer

A)  0.25c 
B)  0.50c 
C)  0.87c 
D)  c 
E)  unknown unless its mass is given 
A)  0.25c 
B)  0.50c 
C)  0.87c 
D)  c 
E)  unknown unless its mass is given

Question 19

The magnitude of the momentum of a particle can never exceed:

Accepted Answer

A)  mc, where m is its mass 
B)  E/c, where E is its energy 
C)  K/c, where K is its kinetic energy 
D)  none of the above, but there is an upper limit 
E)  none of the above; there is no upper limit 
A)  mc, where m is its mass 
B)  E/c, where E is its energy 
C)  K/c, where K is its kinetic energy 
D)  none of the above, but there is an upper limit 
E)  none of the above; there is no upper limit

Question 20

An electron (m = 9.11 * 10-31 kg) has a speed of 0.95c. The magnitude of its momentum is:

Accepted Answer

A)  2.6 * 10-22 kg . m/s 
B)  2.9 * 10-22 kg .m/s 
C)  6.0 * 10-22 kg . m/s 
D)  8.3 *10-22 kg .m/s 
E)  8.8 * 10-22 kg .m/s 
A)  2.6 * 10-22 kg . m/s 
B)  2.9 * 10-22 kg .m/s 
C)  6.0 * 10-22 kg . m/s 
D)  8.3 *10-22 kg .m/s 
E)  8.8 * 10-22 kg .m/s

Exam 37: Relativity

The velocity of an electron is changed from c/2 in the -x direction to c/2 in the +x direction. As a result, its kinetic energy changes by:

Light from a stationary spaceship is observed, then the spaceship moves directly away from the observer at high speed. As a result, the light seen by the observer has:

The length of a meter stick moving at 0.95c in the direction of its length is measured by simultaneously marking its ends on a stationary axis. As measured by clocks moving with the stick, the time interval between the making of the back mark and the making of the front mark is:

As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9 * 10-8 s later a mark is made on the axis at the back end. The marks are found to be 100 m apart. The rest length of the rocket is:

Frame S' moves in the positive x direction at 0.6c with respect to frame S. A particle moves in the positive x direction at 0.4c as measured by an observer in S'. The speed of the particle as measured by an observer in S is:

Two events occur 100 m apart with an intervening time interval of 0.60 μ\muμ s. The speed of a reference frame in which they occur at the same coordinate is:

While emitting light of proper frequency f0, a source moves to the right with speed c/4 relative to reference frame S. A detector, to the left of the source, measures the frequency to be f, which is greater than f0. This means:

Visible light, with a frequency of 6.0 *1014 Hz, is reflected from a spaceship moving directly away at a speed of 0.90c. The frequency of the reflected waves observed at the source is:

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

A basic postulate of Einstein's theory of relativity is:

A meson when at rest decays 2 μ\muμ s after it is created. If moving in the laboratory at 0.99c, its lifetime according to laboratory clocks would be:

Two events occur 100 m apart with an intervening time interval of 0.37 μ\muμ s. The speed of a clock that measures the proper time between the events is:

Two events occur simultaneously at separated points on the y axis of reference frame S. According to an observer moving in the positive x direction:

A particle with zero mass and energy E carries momentum:

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

Two independent events occur 100 m apart with an intervening time interval of 0.42 μ\muμ s. The proper time in μ\muμ s between the events is:

If the kinetic energy of a particle is equal to its rest energy then its speed must be:

The magnitude of the momentum of a particle can never exceed:

An electron (m = 9.11 * 10-31 kg) has a speed of 0.95c. The magnitude of its momentum 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

Electric Charge

Electric Fields

Gauss Law

Electric Potential

Capacitance

Current and Resistance

Circuits

Magnetic Fields

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

All About Atoms

Conduction of Electricity in Solids

Nuclear Physics

Energy From the Nucleus

Quarks, Leptons, and the Big Bang

Filters

As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9 * 10^-⁸ s later a mark is made on the axis at the back end. The marks are found to be 100 m apart. The rest length of the rocket is:

Two events occur 100 m apart with an intervening time interval of 0.60 $\mu$ s. The speed of a reference frame in which they occur at the same coordinate is:

While emitting light of proper frequency f₀, a source moves to the right with speed c/4 relative to reference frame S. A detector, to the left of the source, measures the frequency to be f, which is greater than f₀. This means:

Visible light, with a frequency of 6.0 *10¹⁴ Hz, is reflected from a spaceship moving directly away at a speed of 0.90c. The frequency of the reflected waves observed at the source is:

A meson when at rest decays 2 $\mu$ s after it is created. If moving in the laboratory at 0.99c, its lifetime according to laboratory clocks would be:

Two events occur 100 m apart with an intervening time interval of 0.37 $\mu$ s. The speed of a clock that measures the proper time between the events is:

Two independent events occur 100 m apart with an intervening time interval of 0.42 $\mu$ s. The proper time in $\mu$ s between the events is:

An electron (m = 9.11 * 10^-³¹ kg) has a speed of 0.95c. The magnitude of its momentum is: