A U-tube contains two liquids in static equilibrium water of density -w-1000 kg-m3 is in the right arm- oil of unknown density - is the left arm as shown in figure- Measurement give - - 135 mm and d- 12-5 mm- The density of oil is -

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Vapour Pressure

A U-tube cont...

Question

A U-tube contains two liquids in static equilibrium water of density $ρ_{w} (= 1000 k g / m^{3})$ is in the right arm, oil of unknown density $ρ$ is the left arm as shown in figure. Measurement give $ℓ = 135 m m$ and $d = 12.5 m m$ . The density of oil is :-

1092 k g / m^{3}

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961 k g / m^{3}

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915 k g / m^{3}

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843 k g / m^{3}

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Solution

The correct option is D $915 k g / m^{3}$
If the pressure at the oil-water interface in the left-arm is p, then the pressure in the right arm at the level of the interface will also be p.

So In the left arm:
$p = p_{o} + ρ g (l + d)$

So In the right arm:
$p = p_{o} + ρ_{w} g (l)$

Equating both equations we get

$ρ = \frac{l ρ_{w}}{l + d}$

putting values :

$ρ = \frac{0.135 \times 1000}{0.135 + 0.0125} = 915 k g / m^{3}$

So density of oil is $915 k g / m^{3}$

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A U-tube contains two liquids in static equilibrium water of density ρw(=1000kg/m3) is in the right arm, oil of unknown density ρ is the left arm as shown in figure. Measurement give ℓ=135mm and d=12.5mm. The density of oil is :-

A U-tube contains two liquids in static equilibrium water of density $ρ_{w} (= 1000 k g / m^{3})$ is in the right arm, oil of unknown density $ρ$ is the left arm as shown in figure. Measurement give $ℓ = 135 m m$ and $d = 12.5 m m$ . The density of oil is :-