JEE Main 20146 April
- Exam
- JEE Main
- Year
- 2014
- Date
- 6 April
- Subject
- Physics
- Chapter
- Mechanical Properties of Fluids
JEE Main 2014 · 6 April · Physics · Mechanical Properties of Fluids
There is a circular tube in a vertical plane. Two liquids which do...
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 90o angle at centre. Radius joining their interface makes an angle α with vertical. Ratio is :
Options
- A\dfrac{1 + sin α}{1 - sin α}
- B\dfrac{1 + cos α}{1 - cos α}
- C
- D\dfrac{1 + sin α}{1 - cos α}
Correct answer
C.
Step-by-step solution
Pressure at common interface of two liquid columns is same.
{\text{d}}_{1} \text{gR} \left[\right]\left[1 - sin α\right]\left[\right] = {\text{d}}_{1} \text{gR} \left[\right]\left[1 - cos α\right]\left[\right] + {\text{d}}_{2} \text{gR} \left[\right]\left[sin α + cos α\right]
{\text{d}}_{1} \left[\right]\left[cos α - sin α\right]\left[\right] = {\text{d}}_{2} \left[\right]\left[sin α + cos α\right]
∴ \dfrac{{\text{d}}_{1}}{} = \dfrac{sin α +}{cos α} = \dfrac{tan α + 1}{}
{\text{d}}_{1} \text{gR} \left[\right]\left[1 - sin α\right]\left[\right] = {\text{d}}_{1} \text{gR} \left[\right]\left[1 - cos α\right]\left[\right] + {\text{d}}_{2} \text{gR} \left[\right]\left[sin α + cos α\right]
{\text{d}}_{1} \left[\right]\left[cos α - sin α\right]\left[\right] = {\text{d}}_{2} \left[\right]\left[sin α + cos α\right]
∴ \dfrac{{\text{d}}_{1}}{} = \dfrac{sin α +}{cos α} = \dfrac{tan α + 1}{}