Question

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

Answer 1

Answer: A)
`6.38(10)^(6) m`

Step-by-step explanation:

The equation for the moment of inertia
`I` of a sphere is:

`I=(2)/(5)mr^(2)` (1)

Where:

`I=9.74(10)^(37)kg m^(2)` is the moment of inertia of the planet (assumed with the shape of a sphere)

`m=5.98(10)^(24)kg` is the mass of the planet

`r` is the radius of the planet

Isolating
`r` from (1):

`r=\sqrt{(5I)/(2m)}` (2)

Solving:

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

Finally:

`r=6381149.077m \approx 6.38(10)^(6) m`

Therefore, the correct option is A.