Question

2. A particular planet has a moment of inertia of 9.74 × 1037 kg•m2 and a mass of 5.98 × 1024 kg. Based on these values, what is the planet’s radius?

Answer 1

Answer:

$6.38\cdot 10^6 m$

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

$I=\frac{2}{5}MR^2$

where

M is the mass

R is the radius

For the planet in the problem, we have

$M=5.98\cdot 10^{24} kg$

$I=9.74\cdot 10^{37} kg\cdot m^2$

Solving the equation for R, we find the radius of the planet:

$R=\sqrt{\frac{5I}{2M}}=\sqrt{\frac{5(9.74\cdot 10^{37}}{2(5.98\cdot 10^{24}}}=6.38\cdot 10^6 m$