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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 `90^@` angle at centre. Radius joining their interface make 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

`Rsinalpha d_(2) + Rcosalpha d_(2) + R(1 - cosalpha)d_(1)`
`= R(1 - sinalpha )d_(1)`
`(sinalpha + cosalpha) d_(2) = d_(1)(cosalpha - sinalpha)`
`rArr (d_(1))/(d_(2)) = (1 + tanalpha)/(1 - tanalpha)`
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