Question

A neutron star has a density equal to that of the nuclear matter. Assuming the star to be spherical, find the radius of a neutron star whose mass is 4.0 $\times {10}^{30}$ kg (twice the mass of the sun).

Answer 1

We know $f=\frac{M}{V}$

$\Rightarrow V=\frac{M}{f}=\frac{4\times {10}^{30}}{2.4\times {10}^{17}}$

$=\frac{1}{0.6}\times {10}^{13}$

$=\frac{1}{6}\times {10}^{14}$

$V=\frac{4}{3}\pi R^3$

$\Rightarrow \frac{1}{6}\times {10}^{14}=\frac{4}{3}\times \pi \times R^3$

$\Rightarrow R_3=\frac{1}{6}\times \frac{3}{4}\times \frac{1}{\pi }\times {10}^{14}$

$\Rightarrow R_3=\frac{1}{8}\times \frac{100}{\pi }\times {10}^{12}$

$\therefore R=\frac{1}{2}\times {10}^4\times 3.17$

$=1.585\times {10}^4=15\text{km}$