Question

In a U tube experiment, a column $AB$ of water is balanced by a column $CD$ of paraffin. The relative density of paraffin is

• A. $\frac{h_2}{h_1}$
• B. $\frac{h_1}{h_2}$
• C. $\frac{h_2-h_1}{h_1}$
• D. $\frac{h_2}{h_1+h_2}$

Answer 1

The correct option is A $\frac{h_2}{h_1}$

Pressure difference due to the same height of the same liquid will always be same.
Hence, in the two arms of the $U-$tube, pressure will be the same at surface $D$ & $B$, as shown in figure.
$p_D=p_B$
Also, surface $C$ and $A$ are open to the atmosphere. Hence, both will have the same pressure ($p_0$)

From, $p_D=p_B$
$p_0+{\rho }_{1}g{h}_1=p_0+{\rho }_{w}g{h}_2$
Here, ${\rho }_1=$ density of paraffin
${\rho }_w=$ density of water
$\Rightarrow \frac{{\rho }_1}{{\rho }_w}=\frac{h_2}{h_1}$
where $\frac{{\rho }_1}{{\rho }_w}=$ relative density of paraffin