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  4. An open-ended U-tube of uniform cross-sectional area contains water (density 103 kg 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 (( h 1/ h 2)) of the heights of the liquid in the two arms is

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Q. An open-ended U-tube of uniform cross-sectional area contains water (density $10^{3} \,kg\, m ^{-3}$ ). 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 $\left(\frac{ h _{1}}{ h _{2}}\right)$ of the heights of the liquid in the two arms isPhysics Question Image

JEE AdvancedJEE Advanced 2020

Solution:

image
$800 \times 0.1+1000 \times x=1000 \times(0.58-x)$
$2000 \,x=500$
$x=0.25 \,m$
So, $h_{1}=0.35\, m , h_{2}=0.33 \,m$
$\frac{h_{1}}{h_{2}}=\frac{35}{33}$