Question

What is the average density of a neutron star that has the same mass as the sun but a radius of only 20.0 km?

Answer 1

Answer: $5.935(10)^{13}g/cm^{3}}$

Explanation:

Density is a characteristic property bodies and materials, and is defined as the relationship between the mass $m$ and the volume $V$, as shown below:

$D=\frac{m}{V}$  (1)

In the case of the neutron star, we know it has the same mass as the Sun:

$m=1.989(10)^{30}kg$

And its radius is $r=20km$

On the other hand, if we assume this neutron star has a spherical shape, its volume  can be calculated by the following formula:

$V=V_{sphere}=\frac{4}{3}\pir^{3}$   (2)

$V=\frac{4}{3}\pi(20km)^{3}$   (3)

$V=33510.321km^{3}$   (4)

Substituting (4) in (1):

$D=\frac{1.989(10)^{30}kg}{33510.321km^{3}}$  (5)

Finally:

$D=5.935(10)^{25}kg/km^{3}}=5.935(10)^{13}g/cm^{3}}$