Question

A white dwarf star has a density of about 1.0 x 10^9 kg/m^3. If the earth were to suddenly become as dense as a white dwarf star, what would its radius be? The radius of the earth is actually about 6400 km, and its mass is about 6.0 x 10^24 kg.

Answer 1

112744 m

Step-by-step explanation:

`\rho` = new density of earth = density of white dwarf star =
`1*10^(9) kgm^(-3)`

`M` = mass of earth =
`6.0*10^(24) kg`

`V` = Volume of earth

we know that :

mass = density x volume

`M = \rho V\\6.0*10^(24) = (1*10^(9)) V \\V = 6*10^(15) m^(3)`

`R` = Radius of earth

Since the earth is spherical, volume is given as

`V = (4\pi R^(3))/(3) \\6*10^(15) = (4(3.14) R^(3))/(3)\\R = 112744 m`