(b) what would the radius of the earth be if its matter were compressed to the same density as that of a carbon nucleus? (the earth’s average radius is 6.4 103 km, and its average density is 5.5 g cm 3.)

The density of a carbon nucleus from literature is equal to 2.01×10¹⁵ g/cm³. We will have to equate the density of the Earth to this value. First, let's find the mass of the Earth from the given data:

Volume of Earth = 4/3π(6.4×10³ km * 100,000 cm/1 km)³
Volume = 1.098×10²⁷ cm³
Mass of Earth = 5.5 g/cm³ * 1.098×10²⁷ cm³
Mass of Earth = 6.039×10²⁷ g

Then, we equate this with the density of carbon nucleus.
2.01×10¹⁵ g/cm³ =  6.039×10²⁷ g/V
V = 3×10¹² cm³

Let's equate this to the volume of a sphere of the Earth:
V = 3×10¹² cm³ = 4/3*πr³
r = 40.18 cm

The radius of the Earth should be reduced to 40.18 cm.