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A 'U' tube contains oil, carbon tetrachl...

A 'U' tube contains oil, carbon tetrachloride and water as shown in the figure. The density of oil is 0.8 `"g cm"^(-3)` and that of carbon tetrachloride is `1.6"g cm"^(-3)`. If oil and water surfaces are at the same level, find the height of the water column.

Text Solution

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Find the densities of oil, carbon tetrachloride, water from the given information.
Do the oil and water surfaces exist at the same level ?
Consider a point in the left limb of 'U' tube which in at same level as the bottom surface of water in the right limb.
Take levels in the left and right as 'A' and 'B', respectively.
In pressure at the same level in the two limb equal ?
`"i.e., "P_(A)=P_(B)`
`"If yes, then "P_(B)=Cl_(g)" "(1)`
(Take p = `hd_(g))`
Density of water colume = C
The pressure at point 'A' `=P_(A)=` Pressure due to oil and `C Cl_(4)` columns.
Here, `P_(A)=15xxd_("oil"xx)g+(C-15)xxd_(c cl)xxg` (2)
Equate (1) and (2), and obtain the value of 'C'.
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