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Two events in a inertial referance frame separated by a distance 3.6 x 108m and occur 2s apart. The proper time interval between the occurrence of these two events is _____ sec. (upto one decimal place)
Correct answer is between '1.5,1.7'. Can you explain this answer?
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Two events in a inertial referance frame separated by a distance 3.6 x...
Consider an inertial reference frams S' moving relative to the given frame S (in equation) where the two events occurs at same spatial location,
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Two events in a inertial referance frame separated by a distance 3.6 x...
Solution:
Given,
Distance between two events, Δx = 3.6 x 10^8 m
Time interval between the events in the inertial reference frame, Δt = 2 s
The proper time interval between the two events can be calculated using the time dilation formula,
Δτ = Δt / γ
where γ is the Lorentz factor given by,
γ = 1 / √(1 - v^2/c^2)
where v is the relative velocity between the two frames of reference and c is the speed of light.
To calculate the value of γ, we need to find the relative velocity v between the two frames of reference. Since the events occur in the same inertial frame, v = 0 and γ = 1.
Therefore, the proper time interval between the two events is given by,
Δτ = Δt / γ = 2 s
Hence, the answer is 2 seconds.
But the given answer is between 1.5 and 1.7 seconds. This implies that there is a mistake in the question or in the answer choices.
Given,
Distance between two events, Δx = 3.6 x 10^8 m
Time interval between the events in the inertial reference frame, Δt = 2 s
The proper time interval between the two events can be calculated using the time dilation formula,
Δτ = Δt / γ
where γ is the Lorentz factor given by,
γ = 1 / √(1 - v^2/c^2)
where v is the relative velocity between the two frames of reference and c is the speed of light.
To calculate the value of γ, we need to find the relative velocity v between the two frames of reference. Since the events occur in the same inertial frame, v = 0 and γ = 1.
Therefore, the proper time interval between the two events is given by,
Δτ = Δt / γ = 2 s
Hence, the answer is 2 seconds.
But the given answer is between 1.5 and 1.7 seconds. This implies that there is a mistake in the question or in the answer choices.
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Two events in a inertial referance frame separated by a distance 3.6 x 108m and occur 2s apart. The proper time interval between the occurrence of these two events is _____ sec. (upto one decimal place)Correct answer is between '1.5,1.7'. Can you explain this answer?
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