Two non-viscous, incompressible and immiscible liquids of densities \( \rho \) and \( 1.5 \rho \...

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Two non-viscous, incompressible and immiscible liquids of densities \( \rho \) and \( 1.5 \rho \) are poured into the two limbs of a circular tube of radius \( R \) and small cross-section kept fixed in a vertical plane as shown in figure. Each liquid occupies one-fourth the
P circumference of the tube.
\( (1991,4+4 \) M)
W)
(a) Find the angle \( \theta \) that the radius to the interface makes with the vertical in equilibrium position.
(b) If the whole liquid column is given a small displacement from its equilibrium position, show that the resulting oscillations are simple harmonic. Find the time period of these oscillations.
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