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Average density of the earth
- a)does not depend on g
- b)is a complex function of g
- c)is directly proportional to g
- d)is inversely proportional to g
Correct answer is option 'C'. Can you explain this answer?
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Understanding the Average Density of the Earth:
Average density of the Earth is directly proportional to g:
- The average density of the Earth is directly proportional to the acceleration due to gravity, g.
- This relationship can be explained by the formula for the acceleration due to gravity, which is given by g = GM/R^2, where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.
- The average density of the Earth is defined as the total mass of the Earth divided by its total volume.
- Since density is mass divided by volume, we can express the average density of the Earth as ρ = M/V.
- By substituting the expressions for mass and volume into this equation, we get ρ = M/(4/3πR^3), which simplifies to ρ = 3M/(4πR^3).
- Using the formula for acceleration due to gravity, g = GM/R^2, we can rewrite the equation for density as ρ = 3gR^2/(4πG).
- From this equation, it is clear that the average density of the Earth is directly proportional to the acceleration due to gravity, g.
In conclusion, the average density of the Earth is directly proportional to the acceleration due to gravity, g. This relationship can be derived from the formulas for density and acceleration due to gravity, and it helps us understand the physical properties of our planet.
Average density of the Earth is directly proportional to g:
- The average density of the Earth is directly proportional to the acceleration due to gravity, g.
- This relationship can be explained by the formula for the acceleration due to gravity, which is given by g = GM/R^2, where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.
- The average density of the Earth is defined as the total mass of the Earth divided by its total volume.
- Since density is mass divided by volume, we can express the average density of the Earth as ρ = M/V.
- By substituting the expressions for mass and volume into this equation, we get ρ = M/(4/3πR^3), which simplifies to ρ = 3M/(4πR^3).
- Using the formula for acceleration due to gravity, g = GM/R^2, we can rewrite the equation for density as ρ = 3gR^2/(4πG).
- From this equation, it is clear that the average density of the Earth is directly proportional to the acceleration due to gravity, g.
In conclusion, the average density of the Earth is directly proportional to the acceleration due to gravity, g. This relationship can be derived from the formulas for density and acceleration due to gravity, and it helps us understand the physical properties of our planet.
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Average density of the eartha)does not depend on gb)is a complex function of gc)is directly proportional to gd)is inversely proportional to gCorrect answer is option 'C'. Can you explain this answer?
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