- #1

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(a) Show that dp=ρω

^{2}r'dr'.

(b) If the surface of the fluid is at a radius r

_{o}where the pressure is p

_{o}, show that the pressure p at a distance r≥r

_{o}is p=p

_{o}+ρω2(r

^{2}-r

_{o}

^{2})/2.

(c) An object of volume V and density ρ

_{ob}has its centre of mass at a distance R

_{cmob}from the axis. Show that the net horizontal force on the object is ρVω

^{2}R

_{cm}, where R

_{cm}is the distance from the axis to the center of mass of the displaced fluid.

(d) Explain why the object will move inward if ρR

_{cm}>ρ

_{ob}R

_{cmob}and outward if ρR

_{cm}<ρ

_{ob}R

_{cmob}.

(e) For small objects of uniform density, Rcm = Rcmob. What happens to a mixture of small objects of this kind with different densities in an unltracentrifuge?

This was a problem given in Sears and Zemansky (University Physics)

I have solved parts (a) and (b) of this problem completely. But I could not understand (rather visualise) what R

_{cm}, and R

_{cmob}stand for so was unable to proceed further.

Any help in visualising these terms would be of a great help