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3 years ago

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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 th

e 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

1 answer:

SVEN [57.7K]3 years ago

3 0

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× $10^{7}$

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