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

Answer:

112744 m

Explanation:

$\rho$ = new density of earth = density of white dwarf star = $1\times10^{9} kgm^{-3}$

$M$ = mass of earth = $6.0\times10^{24} kg$

$V$ = Volume of earth

we know that :

mass = density x volume

$M = \rho V\\6.0\times10^{24} = (1\times10^{9}) V \\V = 6\times10^{15} m^{3}$

$R$ = Radius of earth

Since the earth is spherical, volume is given as

$V = \frac{4\pi R^{3}}{3} \\6\times10^{15} = \frac{4(3.14) R^{3}}{3}\\R = 112744 m$