STANDARD Physics Density and gravity relation MCQ Question
The acceleration due to gravity g and density of the Earth ρ are related by which of the following relations? (where G is the gravitational constant and Rₑ is the radius of the Earth)
ρ = 4πGRₑ / 3g
ρ = 3g / 4πGRₑ
ρ = 3G / 4πgRₑ
ρ = 4πgRₑ / 3G
Correct Answer
Detailed Explanation
Using the formula for gravitational acceleration g = GMₑ / Rₑ² and substituting Mₑ = 4/3πRₑ³ρ, we derive ρ = 3g / 4πGRₑ.
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