A vertical $U-$ tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = $1.3 g/cm^3$) column of length $10 $ $cm $ is introduced into one of its arms. Oil of density $0.8 gm/cm^3$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column ........ $cm$. Density of mercury = $13.6 g/cm^3$
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