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 fig. Each liquid occupies one fourth the cirumference of the tube. . (a) Find the angle (theta) that the radius to the interface makes with the verticles in equilibrium position. (b) If the whole is given a small displacement from its equilibrium position, show that the resulting oscillations are simple harmonic. Find the period of these oscillations.

Two non - viscous, incompressible and immiscible liquids of densities

1.	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 fig. Each liquid occupies one fourth the cirumference of the tube. . (a) Find the angle (theta) that the radius to the interface makes with the verticles in equilibrium position. (b) If the whole is given a small displacement from its equilibrium position, show that the resulting oscillations are simple harmonic. Find the period of these oscillations.
Answer» Correct Answer - `theta=(tan^(-1))(1)/(5) = 11.3 ^(@) T=2pisqrt((2.5 pi R)/(g))`

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