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A positive kaon (k+) has a rest mass of 494 MeV/c2 whereas a proton has a rest mass of 938 MeV/c2. If a koan has a total energy that is equal to the proton rest energy, speed of the kaon is most nearly :
- a)0.4 c
- b)0.55 c
- c)0.25 c
- d)0.85 c
Correct answer is option 'D'. Can you explain this answer?
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A positive kaon (k+) has a rest mass of 494MeV/c2whereas a proton has ...
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The correct answer is: 0.85 c
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A positive kaon (k+) has a rest mass of 494MeV/c2whereas a proton has ...
< b="" />Given:< />
- Rest mass of positive kaon (k): 494 MeV/c²
- Rest mass of proton: 938 MeV/c²
- Total energy of kaon = Rest energy of proton
< b="" />To find:< />
- Speed of the kaon when its total energy is equal to the rest energy of a proton.
< b="" />Solution:< />
The total energy (E) of a particle can be calculated using the equation:
E² = (pc)² + (mc²)²
Where:
- E is the total energy
- p is the momentum
- c is the speed of light
- m is the rest mass of the particle
Since the kaon is at rest, its momentum (p) is zero. Therefore, the equation simplifies to:
E = mc²
< b="" />Step 1: Calculate the total energy of the proton:< />
Using the equation E = mc², the total energy of the proton (Ep) is equal to its rest energy, which is 938 MeV.
Ep = 938 MeV
< b="" />Step 2: Calculate the speed of the kaon:< />
Substituting the values into the equation E = mc², we can solve for the speed of the kaon.
E = mc²
494 MeV = (494 MeV/c²) * c² (since E = mc²)
494 MeV = 494 MeV
This means that the total energy of the kaon is equal to its rest energy. However, this does not provide any information about the speed of the kaon.
< b="" />Step 3: Calculate the speed of the kaon using the total energy of the proton:< />
To find the speed of the kaon when its total energy is equal to the rest energy of the proton, we need to use the relationship between energy and velocity.
The total energy (E) of a particle can be related to its momentum (p) and rest mass (m) through the equation:
E² = (pc)² + (mc²)²
Since the momentum of the kaon is zero when it is at rest, the equation simplifies to:
E = mc²
We know that the total energy of the proton (Ep) is equal to its rest energy, which is given as 938 MeV. Using this information, we can solve for the speed of the kaon.
Ep = mc²
938 MeV = (494 MeV/c²) * c²
Dividing both sides of the equation by the rest mass of the kaon (494 MeV/c²), we get:
938 MeV / (494 MeV/c²) = c²
Taking the square root of both sides, we have:
sqrt(938 MeV / (494 MeV/c²)) = c
Calculating the square root and simplifying, we find:
sqrt(1.898) ≈ 1.377
Therefore, the speed of the kaon is approximately 1.377 times the speed of light (c). In terms of the speed of light, the speed of the kaon is approximately 1.377c.
Comparing the options provided, the speed of the kaon is most nearly 0.85c (option D).
- Rest mass of positive kaon (k): 494 MeV/c²
- Rest mass of proton: 938 MeV/c²
- Total energy of kaon = Rest energy of proton
< b="" />To find:< />
- Speed of the kaon when its total energy is equal to the rest energy of a proton.
< b="" />Solution:< />
The total energy (E) of a particle can be calculated using the equation:
E² = (pc)² + (mc²)²
Where:
- E is the total energy
- p is the momentum
- c is the speed of light
- m is the rest mass of the particle
Since the kaon is at rest, its momentum (p) is zero. Therefore, the equation simplifies to:
E = mc²
< b="" />Step 1: Calculate the total energy of the proton:< />
Using the equation E = mc², the total energy of the proton (Ep) is equal to its rest energy, which is 938 MeV.
Ep = 938 MeV
< b="" />Step 2: Calculate the speed of the kaon:< />
Substituting the values into the equation E = mc², we can solve for the speed of the kaon.
E = mc²
494 MeV = (494 MeV/c²) * c² (since E = mc²)
494 MeV = 494 MeV
This means that the total energy of the kaon is equal to its rest energy. However, this does not provide any information about the speed of the kaon.
< b="" />Step 3: Calculate the speed of the kaon using the total energy of the proton:< />
To find the speed of the kaon when its total energy is equal to the rest energy of the proton, we need to use the relationship between energy and velocity.
The total energy (E) of a particle can be related to its momentum (p) and rest mass (m) through the equation:
E² = (pc)² + (mc²)²
Since the momentum of the kaon is zero when it is at rest, the equation simplifies to:
E = mc²
We know that the total energy of the proton (Ep) is equal to its rest energy, which is given as 938 MeV. Using this information, we can solve for the speed of the kaon.
Ep = mc²
938 MeV = (494 MeV/c²) * c²
Dividing both sides of the equation by the rest mass of the kaon (494 MeV/c²), we get:
938 MeV / (494 MeV/c²) = c²
Taking the square root of both sides, we have:
sqrt(938 MeV / (494 MeV/c²)) = c
Calculating the square root and simplifying, we find:
sqrt(1.898) ≈ 1.377
Therefore, the speed of the kaon is approximately 1.377 times the speed of light (c). In terms of the speed of light, the speed of the kaon is approximately 1.377c.
Comparing the options provided, the speed of the kaon is most nearly 0.85c (option D).
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A positive kaon (k+) has a rest mass of 494MeV/c2whereas a proton has a rest mass of 938MeV/c2. If a koan has a total energy that is equal to the proton rest energy, speed of the kaon is most nearly :a)0.4cb)0.55cc)0.25cd)0.85cCorrect answer is option 'D'. Can you explain this answer? for Physics 2026 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A positive kaon (k+) has a rest mass of 494MeV/c2whereas a proton has a rest mass of 938MeV/c2. If a koan has a total energy that is equal to the proton rest energy, speed of the kaon is most nearly :a)0.4cb)0.55cc)0.25cd)0.85cCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A positive kaon (k+) has a rest mass of 494MeV/c2whereas a proton has a rest mass of 938MeV/c2. If a koan has a total energy that is equal to the proton rest energy, speed of the kaon is most nearly :a)0.4cb)0.55cc)0.25cd)0.85cCorrect answer is option 'D'. Can you explain this answer?.
A positive kaon (k+) has a rest mass of 494MeV/c2whereas a proton has a rest mass of 938MeV/c2. If a koan has a total energy that is equal to the proton rest energy, speed of the kaon is most nearly :a)0.4cb)0.55cc)0.25cd)0.85cCorrect answer is option 'D'. Can you explain this answer? for Physics 2026 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A positive kaon (k+) has a rest mass of 494MeV/c2whereas a proton has a rest mass of 938MeV/c2. If a koan has a total energy that is equal to the proton rest energy, speed of the kaon is most nearly :a)0.4cb)0.55cc)0.25cd)0.85cCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A positive kaon (k+) has a rest mass of 494MeV/c2whereas a proton has a rest mass of 938MeV/c2. If a koan has a total energy that is equal to the proton rest energy, speed of the kaon is most nearly :a)0.4cb)0.55cc)0.25cd)0.85cCorrect answer is option 'D'. Can you explain this answer?.
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