Chapter 17 - Planar Kinetics of a Rigid Body: Force and Acceleration - Section 17.1 - Mass Moment of Inertia - Problems - Page 418: 2

$k_{x}=\sqrt{\frac{I_{x}}{m}}=\sqrt{\frac{5.236*10^{13}}{1.57*10^{10}}}=57.7 mm$

$dm=\rho \pi y^{2}dx=\rho \pi (50x)dx$ $I_{x}=\int \frac{1}{2}y^{2}dm=\frac{1}{2} \int 50x(\rho \pi (50x)dx)=1250\rho \pi (\frac{1}{3}(200)^{3})$ $m=\int dm=\int \pi \rho(50x)dx=25(200)^2 \pi \rho$ $k_{x}=\sqrt{\frac{I_{x}}{m}}=\sqrt{\frac{5.236*10^{13}}{1.57*10^{10}}}=57.7 mm$