An $$open-ended$$ $$U-tube$$ of uniform $$cross-sectional$$ area contains water (density$$ $$103kg$$ m−$$3). 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 m−$$3$$ is added to the left arm until its length is $$0.1$$ m, as shown in the schematic figure below. The ratio $$h1h2of$$ the heights of the liquid in the two arms $$is-$$

Question

An $$open-ended$$ $$U-tube$$ of uniform $$cross-sectional$$ area contains water (density$$ $$103kg$$ m−$$3). 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 m−$$3$$ is added to the left arm until its length is $$0.1$$ m, as shown in the schematic figure below. The ratio $$h1h2of$$ the heights of the liquid in the two arms $$is-$$

Infinity Learn · Accepted Answer

$$h1+h2=0.29$$×$$2+0.1h1+h2=0.68$$        ……$$1$$ρ$$k=$$ density of kerosene &ρ$$w=$$ density of water ⇒$$P0+$$ρ$$kg0.1+$$ρ$$wgh1$$−$$0.1$$−ρ$$wgh2=P0$$⇒ρ$$kg0.1+$$ρ$$wgh1$$−ρwg×$$0.1=$$ρ$$wgh2$$⇒$$800$$×$$10$$×$$0.1+1000$$×$$10$$×$$h1$$−$$1000$$×$$10$$×$$0.1=1000$$×$$10$$×$$h2$$⇒$$10000h1$$−$$h2=200$$⇒$$h1$$−$$h2=0.02$$ …….(2)⇒$$h1=0.35$$⇒$$h2=0.33$$ So, $$h1h2=3533$$

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