What is the distance from axis about which a uniform, balsa-wood sphere will have the same moment of inertia as does a thin-walled, hollow, lead sphere of the same mass and radius r, with the axis along a diameter, to the center of the balsa-wood sphere?

≈ 2.1 R

Explanation:

The moment of inertia of the bodies can be calculated by the equation

     I = ∫ r² dm

For bodies with symmetry this tabulated, the moment of inertia of the center of mass

Sphere               = 2/5 M R²

Spherical shell   = 2/3 M R²

The parallel axes theorem allows us to calculate the moment of inertia with respect to different axes, without knowing the moment of inertia of the center of mass

    I = + M D²

Where M is the mass of the body and D is the distance from the center of mass to the axis of rotation

Let's start with the spherical shell, axis is along a diameter

     D = 2R

    Ic = + M D²

    Ic = 2/3 MR² + M (2R)²

    Ic = M R² (2/3 + 4)

    Ic = 14/3 M R²

The sphere

    Is = + M [²

    Is = Ic

    2/5 MR² + M ² = 14/3 MR²

    ² = R² (14/3 - 2/5)

    = √ (R² (64/15)

    = 2,066 R

i just did an experiment like this in my science class. also the answer is yes, it will get separated because they are two opposites meaning if they are opposite they can not attract.

hope this .!

float.

archimedes' principle

denser than water sinks in water.

denser than mercury would sink in it