Answer:
[tex]r=97.22x10^{3} m[/tex]
Explanation:
Using the angular formulas can determine the radius using both values neutron star and the the knowing star so
[tex]L=I*w[/tex]
[tex]L_{1}=I_{1}*w_{1}=L_{2}=I_{2}*w_{2}[/tex]
[tex]I_{1}*w_{1}=I_{2}*w_{2}[/tex]
I=Inertia of the star
w=angular velocity
[tex]I=\frac{2*m*r^{2}}{5}[/tex]
[tex]w=\frac{2\pi}{t}[/tex]
Notice the angular velocity determinate by the time and the Inertia have the radius value so
[tex]\frac{2}{5}*m*r_{sn}^{2}*\frac{2\pi }{t_{1}}=\frac{2}{5}*m*r_{s}^{2}*\frac{2\pi }{t_{2}}[/tex]
[tex]r_{sn}^{2}*\frac{1}{t_{1}}=r_{s}^{2}*\frac{1}{t_{2}}[/tex]
[tex]r_{sn}^{2}=r_{s}^{2}*\frac{t_{1}}{t_{2}}[/tex]
[tex]t_{1}=0.2s\\t_{2}=30day*\frac{24hr}{1day}*\frac{60minute}{1hr}*\frac{60seg}{1minute}=2.592x10^{6}s[/tex]
[tex]r_{sn}=3.5x10^{8}m*\sqrt{\frac{0.2s}{2.592x^{6}s}}[/tex]
[tex]r_{sn}=97.22x10^{3} m[/tex]
