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A rod has s length 100 cm when rod in in a satellite moving with velocity 0:8c reative to laboratory, what is the length of the rod as defined by an observer (s) in the satellite and (b) in the laboratory?
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A rod has s length 100 cm when rod in in a satellite moving with veloc...
Length Contraction
Length contraction is the phenomenon in which an object appears shorter in the direction of its motion when observed from a frame of reference that is moving relative to the object.
Given Data
Length of the rod in rest frame, l = 100 cm
Velocity of the satellite, v = 0.8c
Solution
(a) Length of the rod as defined by an observer in the satellite
The observer in the satellite is at rest relative to the rod. Therefore, the length of the rod as observed by the observer in the satellite will be equal to its rest length.
Length of the rod as observed by the observer in the satellite, l' = l = 100 cm
(b) Length of the rod as defined by an observer in the laboratory
The observer in the laboratory is in a different frame of reference that is moving relative to the rod. According to the theory of relativity, the length of the rod as observed by the observer in the laboratory will be shorter than its rest length.
The formula for length contraction is given by:
l' = l / γ
where γ is the Lorentz factor given by:
γ = 1 / √(1 - v^2/c^2)
Substituting the given values, we get:
γ = 1 / √(1 - 0.8^2) = 1.67
l' = 100 / 1.67 = 59.88 cm
Therefore, the length of the rod as defined by an observer in the laboratory is 59.88 cm.
Conclusion
The length of the rod appears shorter when observed from a frame of reference that is moving relative to the object. This phenomenon is known as length contraction and is an important consequence of the theory of relativity.
Length contraction is the phenomenon in which an object appears shorter in the direction of its motion when observed from a frame of reference that is moving relative to the object.
Given Data
Length of the rod in rest frame, l = 100 cm
Velocity of the satellite, v = 0.8c
Solution
(a) Length of the rod as defined by an observer in the satellite
The observer in the satellite is at rest relative to the rod. Therefore, the length of the rod as observed by the observer in the satellite will be equal to its rest length.
Length of the rod as observed by the observer in the satellite, l' = l = 100 cm
(b) Length of the rod as defined by an observer in the laboratory
The observer in the laboratory is in a different frame of reference that is moving relative to the rod. According to the theory of relativity, the length of the rod as observed by the observer in the laboratory will be shorter than its rest length.
The formula for length contraction is given by:
l' = l / γ
where γ is the Lorentz factor given by:
γ = 1 / √(1 - v^2/c^2)
Substituting the given values, we get:
γ = 1 / √(1 - 0.8^2) = 1.67
l' = 100 / 1.67 = 59.88 cm
Therefore, the length of the rod as defined by an observer in the laboratory is 59.88 cm.
Conclusion
The length of the rod appears shorter when observed from a frame of reference that is moving relative to the object. This phenomenon is known as length contraction and is an important consequence of the theory of relativity.
Community Answer
A rod has s length 100 cm when rod in in a satellite moving with veloc...
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A rod has s length 100 cm when rod in in a satellite moving with velocity 0:8c reative to laboratory, what is the length of the rod as defined by an observer (s) in the satellite and (b) in the laboratory?
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A rod has s length 100 cm when rod in in a satellite moving with velocity 0:8c reative to laboratory, what is the length of the rod as defined by an observer (s) in the satellite and (b) in the laboratory? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A rod has s length 100 cm when rod in in a satellite moving with velocity 0:8c reative to laboratory, what is the length of the rod as defined by an observer (s) in the satellite and (b) in the laboratory? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rod has s length 100 cm when rod in in a satellite moving with velocity 0:8c reative to laboratory, what is the length of the rod as defined by an observer (s) in the satellite and (b) in the laboratory?.
A rod has s length 100 cm when rod in in a satellite moving with velocity 0:8c reative to laboratory, what is the length of the rod as defined by an observer (s) in the satellite and (b) in the laboratory? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A rod has s length 100 cm when rod in in a satellite moving with velocity 0:8c reative to laboratory, what is the length of the rod as defined by an observer (s) in the satellite and (b) in the laboratory? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rod has s length 100 cm when rod in in a satellite moving with velocity 0:8c reative to laboratory, what is the length of the rod as defined by an observer (s) in the satellite and (b) in the laboratory?.
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