The bottom quarter of a vertical cylindrical tank of total height 0.4 m and diameter 0.3 m

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The bottom quarter of a vertical cylindrical tank of total height 0.4 m and diameter 0.3 m is filled with a liquid (SG > 1, like glycerin) and the rest with water, as shown in the figure. The tank is now rotated about its vertical axis at a constant angular speed of ω. Determine 

(a) The value of the angular speed when the point P on the axis at the liquid-liquid interface touches the bottom of the tank

(b) The amount of water that would be spilled out at this angular speed.

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