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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 the vessel is 5 cm and the angular speed of rotation is \omega \; rad \; s^{-1}.The difference in the height, h (in cm) of liquid at the center of vessel and at the side will be:
Option: 1 \frac{2\omega ^{2}}{25g}
Option: 2 \frac{5\omega ^{2}}{2g}
Option: 3 \frac{25\omega ^{2}}{2g}  
Option: 4 \frac{2\omega ^{2}}{5g}

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\begin{aligned} &\text { Applying Bernoulli's equation from } A \text { to } B\\ &P_{0}+\rho \cdot \frac{ V^{2}}{2} -\rho g h=P_{0}\\ &P_{0}+\rho \cdot \frac{ \omega^{2}R^2}{2} -\rho g h=P_{0}\\ &\Rightarrow \frac{\rho R^{2} \omega^{2}}{2}=\rho g h\\ &\Rightarrow \mathrm{h}=\frac{\mathrm{R}^{2} \omega^{2}}{2 \mathrm{~g}}=(5)^{2} \frac{\omega^{2}}{2 \mathrm{~g}}=\frac{25}{2} \frac{\omega^{2}}{\mathrm{~g}} \end{aligned}

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