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Problem $03\mathrm{.}129-$ Two vertical and connected cylindrical tanks

Two vertical and connected cylindrical tanks of diameter $D$ are open to the atmosphere and they contain water at a height

of $h$ in the initial state, as shown in the figure. As the radial blades in the left tank are rotated about the centerline of the

tank$,$ some water in the right tank flows into the left tank. Assume water in the tanks would not spill. Consider

$D=2R=45cm,h=37cm,$ and $g=9\mathrm{.}81\frac{m}{s^2}.$

Problem $03\mathrm{.}129.$b $-$ Max angular velocity of blades on connected cylindrical tanks

Which of the following is a general relation for angular velocity as a function of initial height of water in the tank, assuming that the water in the tanks would not spill?

Multiple Choice

$=\sqrt[\phantom{2}]{\frac{2H}{R}}$

$=\sqrt[\phantom{2}]{\frac{2r}{R^2}}$

$=\frac{2gH}{R^2}$

$=\sqrt[\phantom{2}]{\frac{2gH}{R^2}}$