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An open cylindrical vessel filled with water is rotated together with water at angular speed 1 rad s - 1 . At this angular speed, the centre of the bottom is just exposed. If the angular speed is increased to 3 2 rad s - 1 , how much area (in cm 2 ) of the bottom of the vessel is now exposed to surrounding? [Area of the cross-section of cylinder is 27 cm 2 ]

Correct answer

9

Step-by-step solution

Let ω 1 be initial angular velocity ω 1 2 R 2 2 g = h For angular velocity ω 2 let radius of exposed surface be x ω 2 2 2 g R 2 - x 2 = h Putting the value of ω 1 and ω 2 π x 2 = 9 Since π R 2 = 27

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