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In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain?
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In a system of units in which velocity of light is c=1, which of the f...
Explanation:
Lorentz transformation is a set of equations that relate the coordinates of an event as measured by two observers in relative motion. It is a fundamental concept in special relativity, which describes the relationship between space and time.
The Lorentz transformation can be written as:
x' = γ(x - vt)
y' = y
z' = z
t' = γ(t - vx/c^2)
where γ is the Lorentz factor, given by:
γ = 1/√(1 - v^2/c^2)
where v is the relative velocity between the two observers.
Let's see which of the given options matches the Lorentz transformation:
Option (a):
x' = 4x
y' = y
z' = z'
t' = 0.25t
This transformation does not involve any velocity term and the time coordinate is not consistent with the Lorentz transformation.
Option (b):
x' = x - 0.5t
y' = y
z' = z
t' = t
This transformation is a Galilean transformation, which does not take into account the effects of special relativity.
Option (c):
x' = 1.25x - 0.75t
y' = y
z' = z
t' = 0.75t - 1.25x
This transformation involves velocity terms but does not satisfy the Lorentz transformation.
Option (d):
x' = 1.25x - 0.75t
y' = y
z' = z
t' = 1.25t - 0.75x
This transformation involves velocity terms and satisfies the Lorentz transformation. Therefore, the correct answer is option (d).
Conclusion:
Option (d) is the Lorentz transformation, which relates the coordinates of an event as measured by two observers in relative motion. It involves velocity terms and satisfies the Lorentz transformation.
Lorentz transformation is a set of equations that relate the coordinates of an event as measured by two observers in relative motion. It is a fundamental concept in special relativity, which describes the relationship between space and time.
The Lorentz transformation can be written as:
x' = γ(x - vt)
y' = y
z' = z
t' = γ(t - vx/c^2)
where γ is the Lorentz factor, given by:
γ = 1/√(1 - v^2/c^2)
where v is the relative velocity between the two observers.
Let's see which of the given options matches the Lorentz transformation:
Option (a):
x' = 4x
y' = y
z' = z'
t' = 0.25t
This transformation does not involve any velocity term and the time coordinate is not consistent with the Lorentz transformation.
Option (b):
x' = x - 0.5t
y' = y
z' = z
t' = t
This transformation is a Galilean transformation, which does not take into account the effects of special relativity.
Option (c):
x' = 1.25x - 0.75t
y' = y
z' = z
t' = 0.75t - 1.25x
This transformation involves velocity terms but does not satisfy the Lorentz transformation.
Option (d):
x' = 1.25x - 0.75t
y' = y
z' = z
t' = 1.25t - 0.75x
This transformation involves velocity terms and satisfies the Lorentz transformation. Therefore, the correct answer is option (d).
Conclusion:
Option (d) is the Lorentz transformation, which relates the coordinates of an event as measured by two observers in relative motion. It involves velocity terms and satisfies the Lorentz transformation.
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In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain?
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In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain?.
In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain?.
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In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain?, a detailed solution for In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain? has been provided alongside types of In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain? theory, EduRev gives you an
ample number of questions to practice In a system of units in which velocity of light is c=1, which of the following is a Lorentz transformation? a. x'=4x, y'=y, z=z', t'=0.25t b. x'=x - 0.5t, y'=y, z'=z, t'=t x c. x'=1.25x - 0.75t, y'=y, z'=z, t'=0.75t-1.25x d. x'=1.25x-0.75t, y'=y ,z'=z, t'=1.25t-0.75x Correct answer is option (d) explain? tests, examples and also practice IIT JAM tests.
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