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? Hint: Because planets are the shape of a sphere, the moment of inertia is I = (2/5)mr2.

A) 6.38 x 106 m
B) 2.55 × 106 m
C) 6.52 × 1012 m
D) 4.07 × 1013m

Question

contestada

Respuesta :

cryssatemp cryssatemp · Answer 1 · 2019-08-18T11:00:38+02:00

Answer: A) [tex]6.38(10)^{6} m[/tex]

Explanation:

The equation for the moment of inertia [tex]I[/tex] of a sphere is:

[tex]I=\frac{2}{5}mr^{2}[/tex] (1)

Where:

[tex]I=9.74(10)^{37}kg m^{2}[/tex] is the moment of inertia of the planet (assumed with the shape of a sphere)

[tex]m=5.98(10)^{24}kg[/tex] is the mass of the planet

[tex]r[/tex] is the radius of the planet

Isolating [tex]r[/tex] from (1):

[tex]r=\sqrt{\frac{5I}{2m}}[/tex] (2)

Solving:

[tex]r=\sqrt{\frac{5(9.74(10)^{37}kg m^{2})}{2(5.98(10)^{24}kg)}}[/tex] (3)

Finally:

[tex]r=6381149.077m \approx 6.38(10)^{6} m[/tex]

Therefore, the correct option is A.