Answer:
[tex]6.38\cdot 10^6 m[/tex]
Explanation:
The planet can be thought as a solid sphere rotating around its axis. The moment of inertia of a solid sphere rotating arount the axis is
[tex]I=\frac{2}{5}MR^2[/tex]
where
M is the mass
R is the radius
For the planet in the problem, we have
[tex]M=5.98\cdot 10^{24} kg[/tex]
[tex]I=9.74\cdot 10^{37} kg\cdot m^2[/tex]
Solving the equation for R, we find the radius of the planet:
[tex]R=\sqrt{\frac{5I}{2M}}=\sqrt{\frac{5(9.74\cdot 10^{37}}{2(5.98\cdot 10^{24}}}=6.38\cdot 10^6 m[/tex]
