Question 1

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.

Accepted Answer

Doubling the momentum of a photon doubles its relativistic total energy because both the energy and momentum of a photon are directly proportional to its frequency (or inversely proportional to its wavelength). Therefore, if the momentum is doubled, the energy also doubles, following the relationship E = pc for photons, where E is energy, p is momentum, and c is the speed of light.

Question 2

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 0.80 c?
A)0.44 T
B)0.60 T
C)1.0 T
D)1.7 T

Accepted Answer

The period of oscillation as measured by a ground observer is given by T. When the mass and spring are moving past the ground observer at a speed of 0.80 c, time is dilated and lengths are contracted due to relativistic effects. Therefore, the period of oscillation as measured by the ground observer will be longer.

The formula for time dilation is:

t' = t / (sqrt(1 - v^2/c^2))

where t is the time interval measured by the ground observer (T), t' is the time interval measured by the moving observer, v is the velocity of the moving observer (0.80 c), and c is the speed of light.

Plugging in the numbers, we get:

t' = T / (sqrt(1 - 0.80^2))

t' = 1.7 T

Therefore, the period of oscillation as measured by the moving observer is 1.7 times longer than the period of oscillation as measured by the ground observer.

Question 3

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

Accepted Answer

Muon experiments have provided strong evidence for the time dilation effect predicted by relativity theory. Muons are subatomic particles that are created in the upper atmosphere and travel at high speeds before decaying. If time dilation did not occur, these muons would decay before reaching the Earth's surface. However, experiments have shown that muons are able to reach the Earth's surface because their internal clocks tick slower due to their high speeds. This is strong evidence for the time dilation effect predicted by relativity theory.

Question 4

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.

Accepted Answer

According to Einstein's Theory of Special Relativity, the laws of physics are identical in all inertial frames of reference, regardless of their relative velocities. This is known as the principle of relativity. Therefore, the correct choice is D.

Question 5

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.

Accepted Answer

The Michelson-Morley experiment aimed to detect the motion of the Earth through the hypothetical luminiferous ether that was believed to be the medium for light waves. The results showed that there is no detectable effect of this motion on the speed of light, which supports the idea that the speed of light is constant and independent of the observer's motion. Therefore, the constancy of the speed of light in all inertial frames is consistent with the results of the Michelson-Morley experiment.

Question 6

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.

Accepted Answer

The speed of light is commonly defined as one light-year per year, which is approximately 5.88 trillion miles per year (or 299,792,458 meters per second). Option A is a random number with no relevance to the speed of light, and option B is too small of a measurement for the speed of light. Therefore, option C is the best choice.

Question 7

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.

Accepted Answer

The Michelson-Morley experiment found no effect, meaning that there was no measurable difference in the speed of light in different directions, which was unexpected if there was an ether wind. This result challenged the prevailing theory of the existence of a luminiferous ether and paved the way for the development of Einstein's theory of special relativity.

Question 8

The period of a pendulum is 2.0 s in a stationary inertial frame of reference.What is its period when measured by an observer moving at a speed of 0.60 c with respect to the inertial frame of reference?
A)1.2 s
B)1.6 s
C)2.5 s
D)3.3 s

Accepted Answer

According to time dilation, the period of the pendulum as measured by the moving observer will be longer than the period measured by the stationary observer. The formula for time dilation is:
t' = t/√(1-v^2/c^2)
where t' is the measured time by the moving observer, t is the time measured by the stationary observer, v is the velocity of the moving observer, and c is the speed of light.
Plugging in the given values, we get:
t' = 2/√(1-(0.60c)^2/c^2)
t' = 2/√(1-0.36)
t' = 2/√0.64
t' = 2/0.8
t' = 2.5 s
Therefore, the period of the pendulum as measured by the moving observer is 2.5 s. The best choice is C.

Question 9

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)0.45
B)0.71
C)0.82
D)1.4

Accepted Answer

The answer of The observed relativistic length of a super...

Question 10

The period of an oscillating weight on a spring in an inertial frame of reference is 0.80 s.What would be its speed if it were to move by an observer who measures its period as 1.2 s? (c = 3.00 * 10⁸ m/s) A)1.1 * l0⁸m/s B)2.2 * 10⁸ m/s C)2.5 * l0⁸ m/s D)2.9 * 10⁸ m/s

Accepted Answer

The answer of The period of an oscillating weight on...

Question 11

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.

Accepted Answer

Einstein's theory of relativity is based on two postulates: the principle of relativity (the laws of physics are the same for all non-accelerating observers) and the invariance of the speed of light (the speed of light in a vacuum is the same for all observers regardless of the motion of the light source or the observer). Choice D specifically addresses the invariance of the speed of light, making it the correct answer. A, B, and C are not directly related to the postulates of relativity.

Question 12

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

Accepted Answer

According to the special theory of relativity, as the velocity of an inertial frame of reference increases with respect to an observer, the observed time interval between two events occurring in that frame (from the perspective of the observer) increases. This phenomenon is known as time dilation.

Question 13

A tuning fork has a frequency of 400 Hz and hence a period of 2.50 * 10^-3s.If the tuning fork is in an inertial frame of reference moving by the observer at speed of 0.750 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)265 Hz B)302 Hz C)454 Hz D)605 Hz

Accepted Answer

We can use the relativistic Doppler shift formula for the frequency shift of a wave emitted by a moving source, which is:
f' = f * sqrt((c+v)/(c-v))
where f is the frequency of the wave in the rest frame of the source, f' is the frequency measured by the observer, c is the speed of light, and v is the speed of the source relative to the observer.

Plugging in the given values, we get:
f' = 400 Hz * sqrt((3c/4c)/(c/4c)) = 265 Hz

Therefore, the correct choice is A) 265 Hz.

Question 14

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

Accepted Answer

The Michelson-Morley experiment utilized interference fringes created by splitting and then recombining light beams to detect the Earth's motion through the supposed luminiferous ether, which was believed to be the medium for light waves.

Question 15

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.

Accepted Answer

The answer of I am stationary in a reference system...

Question 16

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.

Accepted Answer

The Michelson-Morley experiment, conducted in 1887, was designed to measure the speed of the Earth's motion through the hypothetical "ether" that was believed to be the medium of light waves. The result of the experiment was unexpected, as it showed that the speed of light was the same in all directions, regardless of the Earth's motion. This led to the theory of special relativity, which postulates that the speed of light is constant and independent of the observer's motion.

Question 17

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

Accepted Answer

The main result of the Michelson-Morley experiment was that no difference in the measured speed of light was observed regardless of the speed of the source or observer's location, contradicting the prevailing theory of an "ether" through which light traveled.

Question 18

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

Accepted Answer

According to the special theory of relativity, the length of an object measured in the dimension parallel to the motion of its inertial frame of reference decreases as the velocity of this frame increases with respect to a stationary observer. This phenomenon is known as length contraction or Lorentz contraction. It is important to note that this effect is only noticeable at velocities close to the speed of light.

Question 19

A ground observer measures the period of a pendulum moving as a part of an inertial frame of reference to be 2.30 s as the inertial frame moves by at a velocity of 0.600 c.What would the observed period be of the same pendulum if its inertial frame were at rest with respect to the observer?
A)4.25 s
B)2.07 s
C)3.03 s
D)1.84 s

Accepted Answer

The answer of A ground observer measures the period of...

Question 20

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

Accepted Answer

According to the theory of relativity, time dilation occurs at speeds close to that of light, meaning time slows down for the moving object. Therefore, although 20 years would have passed on earth, the astronaut would have experienced less time due to time dilation, resulting in a biological age less than 50 years upon returning.

Quiz 26: Relativity

Doubling the momentum of:

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 0.80 c?

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

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?

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

The speed of light is equal to:

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

The period of a pendulum is 2.0 s in a stationary inertial frame of reference.What is its period when measured by an observer moving at a speed of 0.60 c with respect to the inertial frame of reference?

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?

The period of an oscillating weight on a spring in an inertial frame of reference is 0.80 s.What would be its speed if it were to move by an observer who measures its period as 1.2 s? (c = 3.00 * 108 m/s)

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

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?

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

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:

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

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

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 ground observer measures the period of a pendulum moving as a part of an inertial frame of reference to be 2.30 s as the inertial frame moves by at a velocity of 0.600 c.What would the observed period be of the same pendulum if its inertial frame were at rest with respect to the observer?

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?

The period of an oscillating weight on a spring in an inertial frame of reference is 0.80 s.What would be its speed if it were to move by an observer who measures its period as 1.2 s? (c = 3.00 * 10⁸ m/s)