Heavy mass vs light mass in circular motion

[technotux]

Homework Statement

If I have 2 spheres with different mass in a spinning Y shaped tube(no water is in the tube),
https://i.stack.imgur.com/KG7E7m.png
https://i.stack.imgur.com/GE79gm.png

which one will go higher because of inertia and centripetal force, the light sphere or the heavy sphere?

Or if I have 2 masses, a light one and a heavy one on opposite sides but at the same distance from the centre of a spinning table, which mass will move farther from the centre the heavy one or the light one?
https://i.stack.imgur.com/vM5ztm.png

Relevant Equations

f=ma
a=(V^2)/r

i think that the light sphere will go up higher(will have bigger acceleration) because there has to be a balance between the mass and the acceleration as long as the force is the same,

for example if you push a heavy object and with the same force pushed another light object the light object will travel farther(will have more acceleration): let us assume the force=2N, and mass A=4kg, mass B=2kg,

acceleration of mass(A)
a_A=fm=24=0.5m/s2

acceleration of mass(B)
a_B=fm=22=1m/s2

But in a centrifuge, denser substances and particles in the solution move outward in the radial direction. At the same time, objects that are less dense move to the centre?

 

[Orodruin]

as the force is the same,

What force is the same?

 

[Lnewqban]

Welcome!
For the forst two cases, gravity is limiting the movement of the masses.
What is doing so for the third case?

 

[kuruman]

The reason why the two beads on the Y-shaped contraction settle where they do is different from the reason why particles in a centrifuge settle where they do in the sense that different mechanisms are at work for reaching dynamic equilibrium. Consider the first case. For a bead to move around in a horizontal circle, there must be no net vertical force. You know that the Earth exerts a down force which is proportional to the mass of each bead. Therefore there must be an "up" force acting on each bead to cancel the down force of the Earth. Clearly that force must be greater on the heavier bead. Where does this force come from? How does it happen that gravity is matched precisely and separately for each bead? It can all be done with F_net = ma and a free body diagram.

 

[hmmm27]

i think that the light sphere will go up higher(will have bigger acceleration) because there has to be a balance between the mass and the acceleration as long as the force is the same,

If the force spinning the y-tube has a magnitude of 3, and the spheres have masses of 1 and 2, how much force is being applied to the spheres added up ? separately ? Remember Newton.