Speed/velocity of particles inside a centrifuge

[CoolGod]

Which particle experiences the largest centripetal
force in a centrifuge? (3.3) K/U T/I
(a) a 0.05 g particle at a distance of 2 cm from
the centre
(b) a 0.05 g particle at a distance of 5 cm from
the centre
(c) a 0.1 g particle at a distance of 2 cm from
the centre
(d) a 0.1 g particle at a distance of 5 cm from
the centre

from our nelson gr.12 physics textbook. Book says answer is c, logically this means there is a difference in angular velocity between particles with different distance to center because centripetal acceleration= centrifugal acceleration =4pi^2*r(distance to center)*f^2(frequency)

I was wondering in a centrifuge, how are the speed/angular velocity of the particles in relation to their distance to the center of the centrifuge? Is there a formula?

 

[haruspex]

seems to me that in steady state all the particles should have the same angular velocity. There are no tangential forces to maintain a differential. On that basis the answer should be (d), as you have noticed. Mistakes happen.

 

[ap123]

Centripetal Force = mv^2/r = mrω^2 (using v=rω)

All the particles have the same angular speed, so the particle having the largest value of mr will experience the largest centripetal acceleration.

So, the answer looks like (d) and not (c).