The limbs of a `U`-tube are lowerd into beakes `A` and `B`. A contains water and `B` some other liquid. Density of water is `1g//cm^(3)` . Some air is pumped out from `C` and then this end is closed, as a result of this liquids rise by `10cm` and `12cm` respectively, on the left and right side. which of the following is/are correct?

Options

A. Density of the liquid in `B` is `0.83g//"cc"`
B. The heights raised by water and the other liquid in both the sides will change if beakers are kept at different heights
C. The heights raised by water and the other liquid in both sides will be inependent of the positions of the beakers.
D. Liquid in`B` in denser than water in `A`.

Answer

A, C

Explanation

`P_5=P_6=P_(atm), rho_w=1g//"cc"`
As the pressure is the same at the same horizontal level, so `P_3=P_6=P_(atm) and P_4=P_5=P_(atm)`

Pressure at 1 and 2 should be the same
`For A:P_3=P_1+rho_wgh_1`, where `h_1=10cm`
For `B: P_4=P_2+rho-1gh_2`, where `h_2=12cm`
Sovlve to get `rho_wgh_1=rhogh_2`
or `rho_1=0.83g//"cc"`
So the liquid is less denser than water.
Pressure at 5 and 6 will be atmosphere, which will be independent of the levels of beakers.