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In inertial frame S1 two events occur at the same time and 3c minutes aparts in space. In the inertial frame S', the same events occur at 5c minutes apart. What is the time interval between the events in S' ? (in mins)
Correct answer is '4'. Can you explain this answer?
Verified Answer
In inertial frameS1two events occur at the same time and 3c minutes ap...
In frame 
In frame
In frame
Since 
is an invariant quantity
= 25c2 – 9c2
= 16c2
is an invariant quantity= 25c2 – 9c2
= 16c2
Δt2 = 4c In frame S'
The correct answer is: 4
Most Upvoted Answer
In inertial frameS1two events occur at the same time and 3c minutes ap...
Explanation:
Given:
- Two events occur at the same time in inertial frame S1.
- These events are 3c minutes apart in space in frame S1.
- In frame S, the same events occur 5c minutes apart.
We need to find the time interval between the events in frame S.
Understanding the problem:
To understand the problem, let's consider two observers, A and B, in two different inertial frames: S1 and S.
- Observer A is in frame S1, where the events occur at the same time.
- Observer B is in frame S, where the events occur 5c minutes apart.
Solution:
To find the time interval between the events in frame S, we need to establish a relationship between the time intervals in frames S1 and S.
Let's consider that the time interval between the events in frame S1 is Δt1, and the time interval between the events in frame S is Δt.
We know that the events occur 3c minutes apart in space in frame S1, and 5c minutes apart in frame S. Therefore, we can set up the following equation:
Δt = Δt1 + Δt2
Where Δt2 is the time interval between the events in frame S1 and frame S.
Since the events occur at the same time in frame S1, we can set Δt1 = 0.
Therefore, the equation becomes:
Δt = 0 + Δt2
Given that Δt = 5c, we can solve for Δt2:
5c = 0 + Δt2
Δt2 = 5c
Since the time interval between the events in frame S1 is 3c, and Δt2 = 5c, we can find the time interval between the events in frame S:
Δt = Δt1 + Δt2
Δt = 0 + 5c
Δt = 5c
Therefore, the time interval between the events in frame S is 5c minutes.
However, the correct answer is '4'. There seems to be an error in the provided information or calculation. Please double-check the given values and equations to ensure accuracy.
Given:
- Two events occur at the same time in inertial frame S1.
- These events are 3c minutes apart in space in frame S1.
- In frame S, the same events occur 5c minutes apart.
We need to find the time interval between the events in frame S.
Understanding the problem:
To understand the problem, let's consider two observers, A and B, in two different inertial frames: S1 and S.
- Observer A is in frame S1, where the events occur at the same time.
- Observer B is in frame S, where the events occur 5c minutes apart.
Solution:
To find the time interval between the events in frame S, we need to establish a relationship between the time intervals in frames S1 and S.
Let's consider that the time interval between the events in frame S1 is Δt1, and the time interval between the events in frame S is Δt.
We know that the events occur 3c minutes apart in space in frame S1, and 5c minutes apart in frame S. Therefore, we can set up the following equation:
Δt = Δt1 + Δt2
Where Δt2 is the time interval between the events in frame S1 and frame S.
Since the events occur at the same time in frame S1, we can set Δt1 = 0.
Therefore, the equation becomes:
Δt = 0 + Δt2
Given that Δt = 5c, we can solve for Δt2:
5c = 0 + Δt2
Δt2 = 5c
Since the time interval between the events in frame S1 is 3c, and Δt2 = 5c, we can find the time interval between the events in frame S:
Δt = Δt1 + Δt2
Δt = 0 + 5c
Δt = 5c
Therefore, the time interval between the events in frame S is 5c minutes.
However, the correct answer is '4'. There seems to be an error in the provided information or calculation. Please double-check the given values and equations to ensure accuracy.
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