Chapter 12, Problem 87E

(a)

To determine

Prove that $dp=\rho {\omega }^{2}r\text{'}dr\text{'}$ using Newton’s second law on volume element.

(b)

To determine

Prove that pressure $p$ at $r\ge r_0$ is $p=p_0+\rho {\omega }^2\left(r^2-r_0{}^2\right)/2$.

(c)

To determine

Prove that the net horizontal force on an object lies at distance $R_{\text{cmob}}$ is from the axis is $\rho V{\omega }^2{R}_{\text{cm}}$.

(d)

To determine

The reason for motion of object in inward direction when $\rho R_{\text{cm}}>{\rho }_{\text{ob}}{R}_{\text{cmob}}$ and in outward direction when $\rho R_{\text{cm}}<{\rho }_{\text{ob}}{R}_{\text{cmob}}$.

(e)

To determine

The observed result for the ultracentrifugation of mixture of small objects with $R_{\text{cm}}=R_{\text{cmob}}$ but with different densities.