Answer
$H = 4.9\times 10^{-7}~m$
Work Step by Step
Let $M$ be the mass of the cylinder.
Let $r$ be the radius of the cylinder.
We can find the height $H$:
$Mg = F$
$Mg = \frac{2I~A}{c}$
$V~\rho~g = \frac{2I~A}{c}$
$\pi~r^2~H~\rho~g = \frac{2~P~\pi~r^2}{\pi~(D/2)^2~c}$
$H = \frac{8~P}{\pi~D^2~c~\rho~g}$
$H = \frac{(8)~(4.60~W)}{(\pi)~(2.60\times 10^{-3}~m)^2~(3.0\times 10^8~m/s)~(1200~kg/m^3)~(9.8~m/s^2)}$
$H = 4.9\times 10^{-7}~m$
