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

`P_0 + rho_g g+ 10 = P_0 + rho_0 gh + rho_m g(10 - h)`
`1.3 xx 10 = 0.8 h + 13.6 (10 - h)`
`12.8 h = 123`
`h = 9.6 cm`.