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A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is ω rad s–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be

$$A) \frac{2\omega^2}{25g}$$

$$B) \frac{5\omega^2}{2g}$$

$$C)\frac{25\omega^2}{5g}$$

$$D) \frac{2\omega^2}{5g}$$

in Physics
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Correct option is A) $$\frac{25\omega^2}{2g}$$

Explaination::

Applying pressure equation from A to B

$$p_o+\rho.\frac{R\omega^2}{2}.R-\rho gh= p_o$$

$$\rho.\frac{R^2\omega^2}{2}=\rho gh$$

$$h=\frac{R^2\omega^2}{2g}=\frac{5^2\omega^2}{2g}=\frac{25\omega^2}{2g}$$

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