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The acceleration due to gravity g and mean density of the earth ρ are related by which of the following relations? (where G is the gravitational constant and R is the radius of the earth.)

Asked in NEET 1995 · g from mass, radius and density

• (1) ρ=(3g)/(4π GR)
• (2) ρ=(3g)/(4π GR³)
• (3) ρ=(4π gR²)/(3G)
• (4) ρ=(4π gR³)/(3G)

Step-by-step solution

Why the other options are wrong

• (2) comes from carries R³ in the denominator; two of those powers cancel against the R² in g=(GM)/(R²).
• (3) comes from inverts the relation and leaves R² in the numerator.
• (4) comes from inverts the relation with R³ on top, which is dimensionally wrong for a density.

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