JEE Main · 2014 · 06 Apr 2014 · Offline · Fluid Mechanics

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities

d_{1}

and

d_{2}

are filled in the tube. Each liquid subtends

9 0^{\circ}

angle at centre. Radius joining their interface makes an angle

α

with vertical. ratio

d_{1} / d_{2}

Answer: (A)

Solution

Balance the pressures where the two liquid columns meet at the lowest level of the tube. With the interface radius tilted at angle

α

to the vertical, the heavier arc pushes down through

d_{1} g R (cos α - sin α)

and the other through

d_{2} g R (cos α + sin α)

, and at equilibrium these are equal:

d_{1} g R (cos α - sin α) = d_{2} g R (cos α + sin α)

. Cancel

g R

and divide top and bottom by

cos α

to get

\frac{d _{1}}{d _{2}} = \frac{cos α + sin α}{cos α - sin α} = \frac{1 + tan α}{1 - tan α}

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option