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A U-tube is partially filled with mercur...

A U-tube is partially filled with mercury. Some water is poured in its one arm and a liquid in the other arm so that the level of mercury in both arms is same. What is the ratio of lengths of water and liquid in the two arms of the U-tube? Density of water = 1000 kg `m^(-3)` and density of liquid = 900 kg `m^(-3)`

Text Solution

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Since the level of mercury in the two arms of the U-tube is same, therefore , Pressure exerted by water column in one arm = pressuer exerted by liquid column in other arm
`h_1d_1g = h_2d_2g`
` rArr h_1/h_2 = d_2/d_1 = (900 kg m^(-3))/(1000 kg m^(-3)) = 9/10`
Hence the ratio of length of water and the liquid is 9:10.
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