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Question

# There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are filled in the tube. Each liquid subtends 90∘ angle at centre. Radius joining their interface makes an angle α with vertical. Ratio d1d2 is:

A
1+tan α1tan α
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B
1+sin α1cos α
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C
1+sin α1sin α
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D
1+cos α1cos α
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Solution

## The correct option is A 1+tan α1−tan αLet the point be O of tube touching the ground. Pressure due to liquid of density d1 on the left side of O = pressure due to liquid of density d2 on the right side of O. d1(R−R sin α)=d1(R−R cos α)+d2(R sin α+R cos α) d1(1 - sinα)=d1(1−cos α)+d2(sin α+cos α) d1−d1sinα=d1−d1cosα+d2(sinα+cosα) d1(cosα−sin α)=d2(sinα+cosα) d1d2=sinα+cosαcosα−sinα=1+tanα1−tanα

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