An open cylindrical vessel filled with water is rotated together...

An open cylindrical vessel filled with water is rotated together with water at angular speed

1rad{s}^{- 1}

. At this angular speed, the centre of the bottom is just exposed. If the angular speed is increased to

\sqrt{\dfrac{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}

]

An open cylindrical vessel filled with water is rotated together with water at angular speed 1rad s ^ - 1 . At this

Correct answer

Step-by-step solution

Let

{\omega}_{1}

be initial angular velocity
An open cylindrical vessel filled with water is rotated together with water at angular speed 1rad s ^ - 1 . At this

\dfrac{{{\omega}_{1}}^{2}{R}^{2}}{2g} = h

For angular velocity

{\omega}_{2}

let radius of exposed surface be x
An open cylindrical vessel filled with water is rotated together with water at angular speed 1rad s ^ - 1 . At this

\dfrac{{{\omega}_{2}}^{2}}{2g}\left[{R}^{2} - {x}^{2}\right] = h

Putting the value of

{\omega}_{1}

and

{\omega}_{2}

\pi{x}^{2} = 9

Since

\pi{R}^{2} = 27

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