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

Accepted Answer

This is a problem of relativistic Doppler effect. We need to use the formula:
f' = fγ(1 ± v/c)
where f is the frequency of the source (tuning fork), f' is the frequency observed by the observer, v is the relative velocity (0.620 c), c is the speed of light, and γ is the Lorentz factor given by:
γ = 1/√(1 - v^2/c^2)

Substituting the given values, we get:
γ = 1/√(1 - (0.620 c)^2/c^2) = 1.5
f' = 300 × 1.5(1 + 0.620) = 300 × 2.79 = 837 Hz (when moving towards the observer)
or
f' = 300 × 1.5(1 - 0.620) = 300 × 0.705 = 211.5 Hz (when moving away from the observer)

Since the tuning fork is moving towards the observer, the frequency observed will be higher than the actual frequency, and the correct answer is the option A with a frequency of 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.

Accepted Answer

The speed of light is commonly expressed as one light-year per year, as it is the distance light travels in one year. Options A and B are not correct because they do not accurately represent the speed of light. Option D is not correct because one of the choices (option C) is correct.

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

Accepted Answer

According to the special theory of relativity, as the velocity of an inertial frame of reference increases with respect to a stationary observer, the length of an object measured in the dimension parallel to the motion of the frame of reference decreases. This is known as length contraction. Therefore, the best choice is B, length decreases. Option A is incorrect because length does not increase. Option C is incorrect because length does not remain constant. Option D is incorrect as it is not a valid statement according to the theory of relativity.

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

Accepted Answer

The Michelson-Morley experiment used interference fringes (produced by splitting a beam of light and then recombining it) to look for a shift in the pattern caused by the motion of the Earth through the luminiferous ether. However, the experiment failed to detect any such shift, leading to the development of Einstein's theory of special relativity. Sound waves and electromagnetic wind were not involved in the experiment.

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

Accepted Answer

The answer of The period of a pendulum is 1.5...

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

Accepted Answer

The speed of the observer relative to the inertial frame can be found using the relativistic Doppler effect formula for time dilation: $v = c \sqrt{1 - \left(\frac{T_0}{T}\right)^2}$, where $T_0$ is the period in the inertial frame (2.5 s), $T$ is the observed period (3.4 s), and $c$ is the speed of light. Plugging in the values, we find that the speed that matches the given conditions is $2.0 \times 10^8 m/s$, which corresponds to choice B.

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

Accepted Answer

According to the theory of relativity, time dilation occurs as an object approaches the speed of light. This means that time appears to pass more slowly for the astronaut relative to observers on Earth. Therefore, the astronaut's biological age would be less than 50 years upon returning to Earth.

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

Accepted Answer

The observed relativistic length contraction can be calculated using the formula $L = L_0\sqrt{1 - v^2/c^2}$, where $L_0$ is the rest length, $v$ is the velocity of the object, and $c$ is the speed of light. Plugging in $v = 0.70c$, we get $L = L_0\sqrt{1 - 0.49} = L_0\sqrt{0.51}$, which is approximately $L = 0.71L_0$.

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.

Accepted Answer

Einstein's theory of relativity is based on two postulates - the constancy of the speed of light in a vacuum and the principle of equivalence. This means that the speed of light is the same for all observers regardless of the velocity of the source, and that the laws of physics are the same in all inertial reference frames. Option A is a consequence of the theory, but is not a postulate. Option B is actually contradicted by the theory, as space and time are relative to the observer's frame of reference. Option C is a principle of classical mechanics and has no direct relevance to relativity.

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

Accepted Answer

The answer of A mass is bouncing on the end...

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.

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 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

Accepted Answer

Time dilation in relativistic mechanics was first verified by the muon experiments. Muons are elementary particles that travel at very high speeds and decay rapidly. At rest, a muon would decay in 2.2 microseconds, but when they are travelling at 0.995c, they will last up to 28 microseconds before decaying. This verifies time dilation and relativistic mechanics.

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.

Accepted Answer

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

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

Accepted Answer

The length contraction formula is L = L₀√(1-v²/c²), where L₀ is the rest length, v is the velocity, and c is the speed of light. Plugging in the values: L = 15.6√(1-(0.740)²) = 10.5 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

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 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.

Accepted Answer

According to the principle of relativity, which is a postulate of Einstein's theory, the laws of physics are the same in all inertial frames of reference. This means that the physical laws governing any process will remain unchanged regardless of the relative motion of the observer. Therefore, Choice D is the correct answer.

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.

Accepted Answer

The Michelson-Morley experiment demonstrated that the speed of light is constant in all directions, which contradicts the concept of an ether through which light supposedly traveled.

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.

Accepted Answer

The Michelson-Morley experiment was an attempt to detect the hypothetical luminiferous ether that light was thought to travel through, but the experiment was unable to detect any ether. This result is consistent with the idea that the speed of light is the same for all inertial frames, as predicted by Albert Einstein's theory of special relativity.

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

Accepted Answer

The Michelson-Morley experiment was designed to measure the speed of light in different directions, while the Earth moved through a hypothetical ether. If the ether existed, the speed of light should have varied depending on which way the apparatus was oriented. However, the experiment found no such difference in the speed of light, leading to the rejection of the concept of ether and the development of the 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.

Accepted Answer

The Michelson-Morley experiment found no effect, indicating that there was no detectable difference in the speed of light as it traveled in different directions, which challenged the prevailing theories of the existence of a luminiferous ether.

Quiz 26: Relativity

The speed of light is equal to:

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?

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

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?

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)

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 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?

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

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?

Doubling the momentum of:

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

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 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?

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?

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?

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

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

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

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