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A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.
The velocity of the car in the garage’s rest frame is
- a)0.4c
- b)0.6c
- c)0.8c
- d)Greater than c
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A car of rest length 5 meters passes through a garage rest length 4 me...
Length contraction: L = L0/γ
with γ = 1/(1 − v2/c2)½
Given for the car, L0 = 5 m and L = 3 m
γ = L0/L = 5/3 = 1/(1 − v2/c2)½
γ² = 25/9 = 1/(1 − v2/c2)
1 − v²/c² = 9/25
v²/c² = 1 − 9/25 = 16/25
v = 4/5 c = 0.8c
with γ = 1/(1 − v2/c2)½
Given for the car, L0 = 5 m and L = 3 m
γ = L0/L = 5/3 = 1/(1 − v2/c2)½
γ² = 25/9 = 1/(1 − v2/c2)
1 − v²/c² = 9/25
v²/c² = 1 − 9/25 = 16/25
v = 4/5 c = 0.8c
Most Upvoted Answer
A car of rest length 5 meters passes through a garage rest length 4 me...
The relativistic Lorentz contraction is a phenomenon in which objects moving at high speeds appear shorter in the direction of motion as observed from a stationary frame of reference.
In this scenario, the car is moving relative to the garage. The rest length of the car is 5 meters, but due to the relativistic Lorentz contraction, it appears shorter when observed from the garage's frame of reference.
According to the equation for Lorentz contraction:
L = L0 * √(1 - (v^2/c^2))
where L is the observed length, L0 is the rest length, v is the velocity of the car, and c is the speed of light.
Let's assume that the car is moving at a significant fraction of the speed of light, such as 0.8c (where c is the speed of light). Plugging in the values:
L = 5 * √(1 - (0.8^2))
L ≈ 5 * √(1 - 0.64)
L ≈ 5 * √(0.36)
L ≈ 5 * 0.6
L ≈ 3
Therefore, the car appears to be 3 meters long in the garage due to the relativistic Lorentz contraction.
In this scenario, the car is moving relative to the garage. The rest length of the car is 5 meters, but due to the relativistic Lorentz contraction, it appears shorter when observed from the garage's frame of reference.
According to the equation for Lorentz contraction:
L = L0 * √(1 - (v^2/c^2))
where L is the observed length, L0 is the rest length, v is the velocity of the car, and c is the speed of light.
Let's assume that the car is moving at a significant fraction of the speed of light, such as 0.8c (where c is the speed of light). Plugging in the values:
L = 5 * √(1 - (0.8^2))
L ≈ 5 * √(1 - 0.64)
L ≈ 5 * √(0.36)
L ≈ 5 * 0.6
L ≈ 3
Therefore, the car appears to be 3 meters long in the garage due to the relativistic Lorentz contraction.
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A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.The velocity of the car in the garage’s rest frame isa)0.4cb)0.6cc)0.8cd)Greater thancCorrect answer is option 'C'. Can you explain this answer?
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A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.The velocity of the car in the garage’s rest frame isa)0.4cb)0.6cc)0.8cd)Greater thancCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.The velocity of the car in the garage’s rest frame isa)0.4cb)0.6cc)0.8cd)Greater thancCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.The velocity of the car in the garage’s rest frame isa)0.4cb)0.6cc)0.8cd)Greater thancCorrect answer is option 'C'. Can you explain this answer?.
A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.The velocity of the car in the garage’s rest frame isa)0.4cb)0.6cc)0.8cd)Greater thancCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.The velocity of the car in the garage’s rest frame isa)0.4cb)0.6cc)0.8cd)Greater thancCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.The velocity of the car in the garage’s rest frame isa)0.4cb)0.6cc)0.8cd)Greater thancCorrect answer is option 'C'. Can you explain this answer?.
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