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If R is the radius of the earth and g is the acceleration due to gravity

If R is the radius of the earth and g is the acceleration due to gravity on the earth surface, the mean density of the earth is

Options

(a) 4πG/3gR
(b) 3πG/4gR
(c) 3g/4πRG
(d)πRg/12G

Correct Answer:

3g/4πRG

Explanation:

Density = Mass/ Volume

= M / (4/3 π R³)

= (gR² / G). x 3/4  (1/π R³) [as g = GM/R²]

= (3/4π G) x (g/R)

=3g/4πRG

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