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JEE Main201815 Apr 2018Morning ShiftPhysicsMechanical Properties of FluidsActual

A thin uniform tube is bent into a circle of radius r in the virtical plane. Equal volumes of two immiscible liquids, whose densities are ₁ and ₂ ( ₁> ₂ ) fill half the circle. The angle between the radius vector passing through the common interface and the vertical is

Options

  1. A= ⁻¹ [ 2 ( ₁- ₂ ₁+ ₂ ) ]
  2. B= ⁻¹ 2 ( ₁+ ₂ ₁- ₂ )
  3. C= ⁻¹ ( ₁ ₂ )
  4. D= ⁻¹ 2 ( ₂ ₁ )

Correct answer

A. = ⁻¹ [ 2 ( ₁- ₂ ₁+ ₂ ) ]

Step-by-step solution

Pressure at interface A must be same from both the sides to be in equilibrium. aligned &( R + R ) ₂ ~g &=( R - R ) ₁ ~g aligned ₁ ₂ = + - = 1+ 1- ₁- ₁ = ₂+ ₂ ( ₁+ ₂ ) = ₁- ₂ = ⁻¹ ( ₁- ₂ ₁+ ₂ ) , soclosest answer is (a)

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