Answer :
The radius of Earth to have the same mass density as matter in a nucleus is 1.80 x 10^3 m.
The density of a body is given by the following expression;
Density = Mass/Volume
Let the radius of Earth be r.
As the earth is a sphere, hence its volume will be 4/3 x π x r^3
So, the equation becomes
Density = Mass/(4/3 x π x r^3)
The mass of the earth is given as 5.98 x 10^24 kg and the density of the nucleus is given to be 2.4 x 10^14 m.
2.4 x 10^14 = 5.98 x 10^24/ (4/3 x 3.14 x r^3)
On Solving the above equation, the radius r comes out to be
r = 1.80 x 10^3 m.
Hence, The radius of Earth to have the same mass density as matter in a nucleus is 1.80 x 10^3 m.
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