Consider mercury (Hg) rotating about a vertical axis with uniform angular velocity w filled in a cylindrical container. The liquid surface is curved. The figure shows a cross sectional view of the curved surface. Ignore surface tension and viscosity.
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Equation of the free surface of mercury will be
[Hint : coordinates of focus for x2 = 4ay is (0,a)]
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At equilibrium find the angle θ made by tangent to the surface at P(x, y) with the horizontal
[Hint : coordinates of focus for x2 = 4ay is (0,a)]
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Obtain ω if the focal length of the mirror formed by shiny liquid surface is 20 cm
[Hint : coordinates of focus for x2 = 4ay is (0,a)]
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