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)`.

Options

A. `10.4 cm`
B. `8.2 cm`
C. `7.2 cm`
D. `9.6 cm`

Answer

D

Explanation

At the condition of equilibrium
Pressure at point `A = pressure at point `B`
`P_(A) = P_(B)`
`implies 10 xx 1.3 xx g = h xx 0.8 xx g + (10-h) xx 13.6 xxg`
By solving we get `h=9.7 cm`.