Question

# There are three different liquids (liquid 1, liquid 2 and liquid 3) having density 13.6 gm/cc., 1.3 gm/cc and 0.8 gm/cc. Liquid 1 is poured in a uniform U-tube, which is kept vertical. Liquid 2 & liquid 3 are poured separately into the two arms till upper surface of liquid 2 & 3 are same. What is the height of liquid 3 if the height of liquid 2 is 16cm?

A

14.4 cm

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B

16 cm

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C

15.4 cm

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D

12.3 cm

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Solution

## The correct option is C 15.4 cm Pressure at A = Pressure at B ⇒ ρ3gh + ρ1g(H - h) = ρ2gH ⇒ ρ3gh - ρ1gh = ρ2gH - ρ1gH ⇒ h(ρ3−ρ1) = H(ρ2−ρ1) ⇒ h = (ρ2−ρ1)(ρ3−ρ1)H = (ρ1−ρ2)(ρ1−ρ3)H = 15.4 cm

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