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Q.

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is

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a

$425 kg m^{- 3}$

b

$800 kg m^{- 3}$

c

$928 kg m^{- 3}$

d

$650 kg m^{- 3}$

answer is C.

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Detailed Solution

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We know,
Pressure at points B and C should be equal $(P_{B} = P_{C})$
$∴ pressure at B, P_{B} = h_{Oil} ρ_{O i l} g + P_{O}$
$h_{oll} = A B = 140 mm$
$\Rightarrow P_{B} = (140 \times 10^{- 3}) (ρ_{oil}) g + P_{0} \dots (1)$
$Pressure at C, P_{C} = h_{water} ρ_{water} g + P_{0}$
$= (130 \times 10^{- 3}) (1000 {kgm}^{- 3}) g + P_{0} \dots . . (2)$
Equation (1) and (3)

$(140 \times 10^{- 3}) (ρ_{oil}) g + P_{0} = (130 \times 10^{- 3}) (1000) g + P_{0}$
$\Rightarrow 140 \times ρ_{oil} = 130 \times 1000$

$\Rightarrow ρ_{oil} = 928 {kgm}^{- 3}$

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A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is