The total pressure on the top of a closed cylindrical vessel of radius (r) completely filled up with liquid of specific weight (w) and rotating at ($$\omega $$) rad/s about its vertical axis, is

The total pressure on the top of a closed cylindrical vessel of radius (r) completely filled up with liquid of specific weight (w) and rotating at ($$\omega $$) rad/s about its vertical axis, is Correct Answer $$\frac{{\pi {\text{w}}{\omega ^2}{{\text{r}}^2}}}{{4{\text{g}}}}$$

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Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. What is the ratio of coconut oil and milk in the final beaker? If contents from four vessels poured in it. I. Vessel B has 10 ml more capacity than vessel A and the ratio of coconut oil and milk in vessel B is 2 ∶ 7. Vessel C has coconut oil and milk in the ratio 2 ∶ 3 and contains 38 ml more capacity than Vessel D II. Vessel A has milk and coconut oil in the ratio 3 ∶ 5. Vessel C has 12 ml more coconut oil than vessel D.
Two monochromatic waves having frequencies $$\omega $$ and $$\omega + \Delta \omega \left( {\Delta \omega \ll \omega } \right)$$    and corresponding wavelengths $$\lambda $$ and $$\lambda - \Delta \lambda \left( {\Delta \lambda \ll \lambda } \right)$$    of same polarization, travelling along X-axis are superimposed on each other. The phase velocity and group velocity of the resultant wave are respectively given by