Question

A U-tube contains water and oil separated by mercury. The mercury columns in the two arms are at the same level with $10\text{cm}$ of water in one arm and $12.5\text{cm}$ of oil in the other, as shown in figure. What is the relative density of oil?

• A. $0.8$
• B. $1.0$
• C. $1.25$
• D. None of these

Answer 1

The correct option is A $0.8$

As we know,
Relative density of oil $=\frac{{\rho }_{\text{oil}}}{{\rho }_w}$
where, ${\rho }_{oil}=$ Density of oil
${\rho }_w=$ Density of water


Since, $A\&B$ are at same level
So, $P_A=P_B$
$\Rightarrow P_0+{\rho }_{w}g\times h_{\text{water}}=P_0+{\rho }_{\text{oil}}g\times h_{\text{oil}}$
$\Rightarrow {\rho }_w\times h_{\text{water}}={\rho }_{\text{oil}}\times h_{\text{oil}}$
$\Rightarrow \frac{{\rho }_{\text{oil}}}{{\rho }_w}=\frac{h_{\text{water}}}{h_{\text{oil}}}=\frac{10}{12.5}=\frac{100}{125}=0.8$