A circular tube of uniform cross section is filled with two liquids densities `rho_(1)` and `rho_(2)` such that half of each liquid occupies a quarter to volume of the tube. If the line joining the free surfaces of the liquid makes an angle `theta` with horizontal find the value of `theta.`

A rectangular tube of uniform cross section has three liquids of densities rho_(1), rho_(2) and rho_(3) . Each liquid column has length l equal to length of sides of the equilateral triangle. Find the length x of the liquid of density rho_(1) in the horizontal limb of the tube, if the triangular tube is kept in the vertical plane.

A rectangular tube of uniform cross section has three liquids of densities rho_(1), rho_(2) and rho_(3) . Each liquid column has length l equal to length of sides of the equilateral triangle. Find the length x of the liquid of density rho_(1) in the horizontal limb of the tube, if the triangular tube is kept in the vertical plane.

A narrow U-tube placed on a horizontal surface contains two liquids of densities rho_(1) and rho_(2) . The columns of the liquids are indicated in the figure. The ratio (rho_(1))/(rho_(2)) is equal to :

A narrow U-tube placed on a horizontal surface contains two liquids of densities rho_(1) and rho_(2) . The columns of the liquids are indicated in the figure. The ratio (rho_(1))/(rho_(2)) is equal to :

The figure represents a U-tube of uniform cross-section filled with two immiscible liquids. One is water with density rho_(w) and the other liquid is of density rho . The liquid interface lies 2 cm above the base. The relation between rho and rho_(w) is .

The figure represents a U-tube of uniform cross-section filled with two immiscible liquids. One is water with density rho_(w) and the other liquid is of density rho . The liquid interface lies 2 cm above the base. The relation between rho and rho_(w) is .

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. Find the angle (theta) that the radius to the interface makes with the verticles in equilibrium position.

A test tube of uniform cross-section is floated vertically in a liquid 'A' (density rho A ) upto a mark on it when it is filled with 'x' ml of a liquid 'B' (density rho B ). To make the test tube float in liquid B upto the same mark it is filled with y ml of the liquid A. Find the mass of the test tube.

A thin uniform circular tube is kept in a vertical plane. Equal volume of two immiscible liquids whose densites are rho_(1) and rho_(2) fill half of the tube as shown. In equilibrium the radius passing through the interface makes an angle of 30^(@) with vertical. The ratio of densities (rho_(1)//rho_(2)) is equal to