Question

A particular planet has a moment of inertia of 8.26 × 1036 kg⋅m2 and a mass of 6.54 × 1022 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.
7.12 × 106 m
1.78 × 107 m
5.05 × 1013 m
3.16 × 1014

Answer 1

Answer: Correct answer is B = 1.776933×$10^{7}$

Explanation:

Given :

Moment of inertia I = 8.26×$10^{36}$ kg$m^{2}$

Mass of planet m = 6.54×$10^{22}$ kg

Also, Planet is solid sphere so that, Moment of inertia is I = $\frac{2}{5}$ m$R^{2}$ =0.4m$R^{2}$

Where R is radius of planet

Putting into calculation

We get,

I = $\frac{2}{5}$ m$R^{2}$

8.26×$10^{36}$ =  0.4×6.54×$10^{22}$×$R^{2}$

8.26×$10^{14}$ = 2.616 $R^{2}$

3.15749235×$10^{14}$ = $R^{2}$

R =  1.776933×$10^{7}$

Thus, Correct answer is B = 1.776933×$10^{7}$