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The ratio of radii of two spheres of metal is 1 : 2. The ratio of the amounts of radiation emitted by them at same temperature will be
- a)1 : 4
- b)1 : 8
- c)2 : 1
- d)8 : 1
Correct answer is option 'A'. Can you explain this answer?
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The ratio of radii of two spheres of metal is 1 : 2. The ratio of the ...
The radiation energy emitted by a body per unit time is given by
Eb = ϵAσT4
Where ϵ is emissivity of the body.
σ = The Stefan – Boltzmann constant = 5.67 × 10-8 W m-2K-4
Calculation:
For same material and same temperature: E ∝ A
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The ratio of radii of two spheres of metal is 1 : 2. The ratio of the ...
The ratio of radii of two spheres is given as 1:2. Let's assume the radii of the two spheres to be r and 2r, where r is the radius of the smaller sphere.
The amount of radiation emitted by a sphere is directly proportional to the surface area of the sphere. The surface area of a sphere is given by the formula:
Surface area = 4πr^2
Let's calculate the surface areas of the two spheres and compare them.
For the smaller sphere with radius r:
Surface area = 4πr^2
For the larger sphere with radius 2r:
Surface area = 4π(2r)^2 = 4π(4r^2) = 16πr^2
Now, let's calculate the ratio of the surface areas of the two spheres:
Ratio of surface areas = (Surface area of larger sphere) / (Surface area of smaller sphere)
= (16πr^2) / (4πr^2)
= 16/4
= 4
So, the ratio of the surface areas of the two spheres is 4:1.
Since the amount of radiation emitted by a sphere is directly proportional to its surface area, the ratio of the amounts of radiation emitted by the two spheres will also be 4:1.
Therefore, the correct answer is option A) 1:4.
The amount of radiation emitted by a sphere is directly proportional to the surface area of the sphere. The surface area of a sphere is given by the formula:
Surface area = 4πr^2
Let's calculate the surface areas of the two spheres and compare them.
For the smaller sphere with radius r:
Surface area = 4πr^2
For the larger sphere with radius 2r:
Surface area = 4π(2r)^2 = 4π(4r^2) = 16πr^2
Now, let's calculate the ratio of the surface areas of the two spheres:
Ratio of surface areas = (Surface area of larger sphere) / (Surface area of smaller sphere)
= (16πr^2) / (4πr^2)
= 16/4
= 4
So, the ratio of the surface areas of the two spheres is 4:1.
Since the amount of radiation emitted by a sphere is directly proportional to its surface area, the ratio of the amounts of radiation emitted by the two spheres will also be 4:1.
Therefore, the correct answer is option A) 1:4.
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The ratio of radii of two spheres of metal is 1 : 2. The ratio of the amounts of radiation emitted by them at same temperature will bea)1 : 4b)1 : 8c)2 : 1d)8 : 1Correct answer is option 'A'. Can you explain this answer?
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