Question

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

Answer 1

Let the length of oil column `=CD=xcm`
Length of glycerine `=AB=10 cm`
`:. DE=(10-x)cm`
Equating pressure at horizontal level `BE` in both arms, we have
`P_("oil")+P_(Hg)=P_("glycerine")`
`xd_("oil")g+(10-x)rho_(Hg)g=10d_("glycerine")g`
or `x(0.8)=(10-x)13.6=10(1.3)impliesx=(136-13)/12.8=9.6cm`