Question 1

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 2

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 3

A consequence of Einstein's theory of relativity is:

Accepted Answer

A)  moving clocks appear to run more slowly than when they are at rest 
B)  moving rods appear 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 appear to run more slowly than when they are at rest 
B)  moving rods appear 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 4

Spaceship A, traveling past us at 0.7c, sends a message capsule to spaceship B, which is in front of A and is traveling in the same direction as A at 0.8c relative to us. The capsule travels at 0.95c relative to us. A clock that measures the proper time between the sending and receiving of the capsule travels:

Accepted Answer

A)  in the same direction as the spaceships at 0.7c relative to us 
B)  in the opposite direction from the spaceships at 0.7c relative to us 
C)  in the same direction as the spaceships at 0.8c relative to us 
D)  in the same direction as the spaceships at 0.95c relative to us 
E)  in the opposite direction from the spaceships at 0.95c relative to us 
A)  in the same direction as the spaceships at 0.7c relative to us 
B)  in the opposite direction from the spaceships at 0.7c relative to us 
C)  in the same direction as the spaceships at 0.8c relative to us 
D)  in the same direction as the spaceships at 0.95c relative to us 
E)  in the opposite direction from the spaceships at 0.95c relative to us

Question 5

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 6

Two events occur on the x axis separated in time by $\Delta$t and in space by $\Delta$x. A reference frame, traveling at less than the speed of light, in which the two events occur at the same coordinate:

Accepted Answer

A)  exists no matter what the values of $\Delta$x and $\Delta$t 
B)  exists only if $\Delta$x/$\Delta$t  c 
D)  exists only if $\Delta$x/$\Delta$t = c 
E)  does not exist under any condition 
A)  exists no matter what the values of $\Delta$x and $\Delta$t 
B)  exists only if $\Delta$x/$\Delta$t  c 
D)  exists only if $\Delta$x/$\Delta$t = c 
E)  does not exist under any condition

Question 7

A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c toward 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 8

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 9

Star S1 is moving away from us at a speed of 0.8c. Star S2 is moving away from us in the opposite direction at a speed of 0.5c. The speed of S1 as measured by an observer on S2 is:

Accepted Answer

A)  0.21c 
B)  0.50c 
C)  0.93c 
D)  1.3c 
E)  2.2c 
A)  0.21c 
B)  0.50c 
C)  0.93c 
D)  1.3c 
E)  2.2c

Question 10

A meter stick moves in the direction of its length through a laboratory. According to measurements taken in the laboratory, its length is 0.31 m. The speed of the meter stick relative to the laboratory is:

Accepted Answer

A)  0.096c 
B)  0.31c 
C)  0.69c 
D)  0.83c 
E)  0.95c 
A)  0.096c 
B)  0.31c 
C)  0.69c 
D)  0.83c 
E)  0.95c

Question 11

Observer A measures the velocity of a rocket as and a comet as . Here and are parallel and in the direction of the observer's positive x axis. The speed of the comet as measured by an observer on the rocket is:

Accepted Answer

A)  (u - v)/(1 - uv/c2) 
B)  (u - v)/(1 - v2/c2) 
C)  (u - v)/(1 - v2/c2)1/2 
D)  (u - v)/(1 + uv/c2) 
E)  (u + v)/(1 - uv/c2) 
A)  (u - v)/(1 - uv/c2) 
B)  (u - v)/(1 - v2/c2) 
C)  (u - v)/(1 - v2/c2)1/2 
D)  (u - v)/(1 + uv/c2) 
E)  (u + v)/(1 - uv/c2)

Question 12

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 at 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 at 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 13

A millionairess was told in 1992 that she had exactly 15 years to live. However, if she immediately takes off, travels away from the Earth at 0.8 c and then returns at the same speed, the last New Year's Day the doctors expect her to celebrate is:

Accepted Answer

A)  2001 
B)  2003 
C)  2007 
D)  2017 
E)  2033 
A)  2001 
B)  2003 
C)  2007 
D)  2017 
E)  2033

Question 14

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 15

A consequence of Einstein's theory of relativity is:

Accepted Answer

A)  moving clocks appear to run faster than when they are at rest 
B)  moving rods appear 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 appear to run faster than when they are at rest 
B)  moving rods appear 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

Question 16

According to relativity theory a particle of mass m with a momentum of 2mc has a speed of:

Accepted Answer

A)  4c 
B)  2c 
C)  c 
D)  0.89c 
E)  c/2 
A)  4c 
B)  2c 
C)  c 
D)  0.89c 
E)  c/2

Question 17

A certain particle has a kinetic energy of 3.2 *10-10 J and a momentum of 1.7 *10-18 kg . m/s. Its mass is:

Accepted Answer

A)  9.1 F* 10-31 kg 
B)  2.7 * 10-27 kg 
C)  4.5 *10-27 kg 
D)  6.3 *10-27 kg 
E)  8.6* 10-27 kg 
A)  9.1 F* 10-31 kg 
B)  2.7 * 10-27 kg 
C)  4.5 *10-27 kg 
D)  6.3 *10-27 kg 
E)  8.6* 10-27 kg

Question 18

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 19

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 20

Two events occur on the x axis separated in time by $\Delta$t and in space by $\Delta$x. A reference frame, traveling at less than the speed of light, in which the two events occur at the same time:

Accepted Answer

A)  exists no matter what the values of $\Delta$x and $\Delta$t 
B)  exists only if $\Delta$x/$\Delta$t  c 
D)  exists only if $\Delta$x/$\Delta$t = c 
E)  does not exist under any condition 
A)  exists no matter what the values of $\Delta$x and $\Delta$t 
B)  exists only if $\Delta$x/$\Delta$t  c 
D)  exists only if $\Delta$x/$\Delta$t = c 
E)  does not exist under any condition

Exam 37: Relativity

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

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:

A consequence of Einstein's theory of relativity is:

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

Two events occur on the x axis separated in time by Δ\DeltaΔ t and in space by Δ\DeltaΔ x. A reference frame, traveling at less than the speed of light, in which the two events occur at the same coordinate:

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

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:

Star S1 is moving away from us at a speed of 0.8c. Star S2 is moving away from us in the opposite direction at a speed of 0.5c. The speed of S1 as measured by an observer on S2 is:

A meter stick moves in the direction of its length through a laboratory. According to measurements taken in the laboratory, its length is 0.31 m. The speed of the meter stick relative to the laboratory is:

Observer A measures the velocity of a rocket as and a comet as . Here and are parallel and in the direction of the observer's positive x axis. The speed of the comet as measured by an observer on the rocket 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:

A millionairess was told in 1992 that she had exactly 15 years to live. However, if she immediately takes off, travels away from the Earth at 0.8 c and then returns at the same speed, the last New Year's Day the doctors expect her to celebrate is:

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

A consequence of Einstein's theory of relativity is:

According to relativity theory a particle of mass m with a momentum of 2mc has a speed of:

A certain particle has a kinetic energy of 3.2 *10-10 J and a momentum of 1.7 *10-18 kg . m/s. Its mass 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:

Two events occur on the x axis separated in time by Δ\DeltaΔ t and in space by Δ\DeltaΔ x. A reference frame, traveling at less than the speed of light, in which the two events occur at the same time:

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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:

Two events occur on the x axis separated in time by $\Delta$ t and in space by $\Delta$ x. A reference frame, traveling at less than the speed of light, in which the two events occur at the same coordinate:

A certain particle has a kinetic energy of 3.2 10^-10 J and a momentum of 1.7 10^-18 kg . m/s. Its mass is:

Two events occur on the x axis separated in time by $\Delta$ t and in space by $\Delta$ x. A reference frame, traveling at less than the speed of light, in which the two events occur at the same time: