Question

A vertical U tube of uniform inner cross-section containing mercury in both its arms. A glycerine ( density $1300kg{m}^{-3}$) column of length $10$ cm is introduced into one of the arms. Oil of density ($800kg{m}^{-3}$) is poured in the other arm until the upper surface of the oil and the glycerine are in the same horizontal surface. Find the length of oil column ( Density of mercury = $13.6\times {10}^{3}kg{m}^{-3}$)

Answer 1

REF.Image.

as point A and B are at

horizontal level,

Pressure at $A=f_{uly}\times g\times \frac{20}{100}$

$P_A=1300\times 10\times \frac{20}{100}$

$P_A=2600N/M^2$

Pressure at B $=foil\times g\times h+fHh\times g\times \frac{(20-h)}{100}$

$P_B=800\times 10\times \frac{h}{100}+13.6\times {10}^3\times 10\times \frac{(20-h)}{100}$

$P_B=80h+1360(20-h)$

As $P_A=P_B$,

$\Rightarrow 2600=80h+27200-1360h$

$\Rightarrow 1280h=27200-2600$

$\Rightarrow 1280h=24600$

$\Rightarrow h=\frac{24600}{1280}=1921875$

$h=19.22cm$

The length of oil column is 19.22 cm.