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A smaller sphere (1) of radius 50 mm is inside a larger sphere (2) of radius 100 mm. What will be the value of the radiation shape factor F22:
- a)3/4
- b)4/3
- c)1.0
- d)Zero
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A smaller sphere (1) of radius 50 mm is inside a larger sphere (2) of...
F11 = 0 and F12 = 1
F21 + F22 = 1
And A1.F12 = A2.F21.F21 = 0.25
It means F22 = 1 - 0.25 = 0.75
Most Upvoted Answer
A smaller sphere (1) of radius 50 mm is inside a larger sphere (2) of...
Explanation:
To find the value of the radiation shape factor F22, we need to consider the geometry of the two spheres and calculate the ratio of the areas.
Given:
Radius of smaller sphere (1) = 50 mm
Radius of larger sphere (2) = 100 mm
Calculation:
The radiation shape factor F22 represents the fraction of radiation emitted by sphere 1 that is intercepted by sphere 2.
The formula for the radiation shape factor F22 is given by:
F22 = A2 / A1
Where:
- A1 is the surface area of sphere 1
- A2 is the surface area of sphere 2
The surface area of a sphere can be calculated using the formula:
A = 4πr^2
Surface area of sphere 1:
A1 = 4π(50)^2
A1 = 4π(2500)
A1 = 10000π
Surface area of sphere 2:
A2 = 4π(100)^2
A2 = 4π(10000)
A2 = 40000π
Calculating the radiation shape factor:
F22 = A2 / A1
F22 = (40000π) / (10000π)
F22 = 4
Therefore, the value of the radiation shape factor F22 is 4.
However, none of the given options match the calculated value of 4. Therefore, the answer provided is incorrect and none of the options are correct.
Correct answer:
None of the given options are correct.
To find the value of the radiation shape factor F22, we need to consider the geometry of the two spheres and calculate the ratio of the areas.
Given:
Radius of smaller sphere (1) = 50 mm
Radius of larger sphere (2) = 100 mm
Calculation:
The radiation shape factor F22 represents the fraction of radiation emitted by sphere 1 that is intercepted by sphere 2.
The formula for the radiation shape factor F22 is given by:
F22 = A2 / A1
Where:
- A1 is the surface area of sphere 1
- A2 is the surface area of sphere 2
The surface area of a sphere can be calculated using the formula:
A = 4πr^2
Surface area of sphere 1:
A1 = 4π(50)^2
A1 = 4π(2500)
A1 = 10000π
Surface area of sphere 2:
A2 = 4π(100)^2
A2 = 4π(10000)
A2 = 40000π
Calculating the radiation shape factor:
F22 = A2 / A1
F22 = (40000π) / (10000π)
F22 = 4
Therefore, the value of the radiation shape factor F22 is 4.
However, none of the given options match the calculated value of 4. Therefore, the answer provided is incorrect and none of the options are correct.
Correct answer:
None of the given options are correct.
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A smaller sphere (1) of radius 50 mm is inside a larger sphere (2) of radius 100 mm. What will be the value of the radiation shape factor F22:a)3/4b)4/3c)1.0d)ZeroCorrect answer is option 'A'. Can you explain this answer?
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