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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)`. |
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Answer» 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` |
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