An Open – ended U-tube of uniform cross-sectional area contains water (density 10^3 kg/m^3) . Initially the water level stands

Q: An Open – ended U-tube of uniform cross-sectional area contains water (density 10³ kg/m³) . Initially the water level stands at 0.29 m from the bottom in each arm . Kerosene oil (a water immiscible liquid) of density 800 kg/m³ is added to the left arm until its length is 0.1 m as shown in figure . The ratio (h₁/h₂) of the height of the liquid in the two arms is

(a) 15/14

(b) 35/33

(c) 7/6

(d) 5/4

Ans: (b)

Sol: As h₁ + h₂ = 0.29 x 2 + 0.1

h₁ + h₂ = 0.68 …(i)

P₀ + ρ_k g (0.1) + ρ_w g (h₁ -0.1) – ρ_w g h₂ = P₀

ρ_k g (0.1) + ρ_w g h₁ – ρ_w g x 0.1 = ρ_w g h₂

800 x 10 x 0.1 + 1000 x 10 x h₁ – 1000 x 10 x 0.1 = 1000 x 10 x h₂

10000 (h₁ -h₂) = 200

h₁ – h₂ = 0.02 …(ii)

Solving (i) & (ii) we get

h₁ = 0.35 m and h₂ = 0.33 m

h₁/h₂ = 35/33