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The cross-sectional area of the left lim...

The cross-sectional area of the left limb of a U-tube is one-third of that of its right limb. It contains some mercury. The empty space in the left limb measures to 40 cm. If water is poured to fill it up, then find the rise of the mercury column in the right limb. (Specific gravity of mercury = 13.6)

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At first, the mercury is at the same level in both the limbs. When water is poured, suppose the fall in the mercury level in the narrow limb is x and the corresponding rise in the mercury level in the wider limb is y.

If the cross-sectional area of the narrow limb is A, then, according to the problem, the cross-sectional area of the wider limb will be 3A.
From Figure we see,
volume of tha part A.C = volume of the part FB
or, `x xxA=yxx3A` or, x = 3y
Now, pressure at point C = pressure at point D
or, `ECxx1xxg=FDxx13.6xxg`
or, `(40+x)=(x+y)xx13.6`
or, `40+3y=(3y+y)xx13.6or,(13.6xx4-3)y=40`
or, `y=40/(54.4-3)=0.78cm`.
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