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Question
Calculate the radius of the earth if the density of the earth is equal to the density of the nucleus. [mass of earth 5.97 x 1024 kg].
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Solution
The density of the nucleus of an atom
ρN = 2.3 x 1017 kg m-3
ρN = ρE = 2.3 x 1017 kg m-3
Mass of the earth ME = 5.97 x 1024 kg
Density of the earth,
`rho_"E" = "m"_"E"/"V"`
`= "m"_"E"/(4/3 pi"r"^3)`
`"r"^3 = "m"_"E"/(4/3 pirho_"E") = (5.97 xx 10^24)/(1.33 xx 3.14 xx 2.3 xx 10^17)`
`= (5.97 xx 10^24)/(9.60526 xx 10^17)`
r3 = 0.62155 x 107 m3
r3 = 183.85 m
r ≈ 180 m.
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