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There is a circular tube in a vertical p...


There is a circular tube in a vertical plane. Two liquids which do not mix and of densiities `d_(1) and d_(2)` are filled I the tube. Each liquid subtends `90^(@)` angle at centre. Radius joining their interface makes an angle `alpha` with vertical. Ratio `d_(1)//d_(2)` is

A

`(1 + sin alpha)/( 1 - sin alpha)`

B

`(1 + cos alpha)/( 1 - cos alpha)`

C

`(1 + tan alpha)/( 1 - tan alpha)`

D

`(1 + sin alpha)/( 1 - cos alpha)`

Text Solution

Verified by Experts

The correct Answer is:
C
Pressure at interface A must be same from both the side to be in equilibrium

`(R cos alpha + R sin alpha ) d_(2) g = (R cos alpha - R sin alpha ) d_(1) g `
`(d_(1))/( d_(2)) = (cos alpha + sin alpha )/( cos alpha - sin alpha ) = (1 + tan alpha )/(1 - tan alpha )`
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