Question

Find the density of the oil inside the U-tube as shown in figure. (Take density of water ${\rho }_w=1000{\text{kg/m}}^3$)

• A. $600{\text{kg/m}}^3$
• B. $400{\text{kg/m}}^3$
• C. $300{\text{kg/m}}^3$
• D. $500{\text{kg/m}}^3$

Answer 1

The correct option is B $400{\text{kg/m}}^3$



Let ${\rho }_o$ be the density of oil.
Given density of water, ${\rho }_w=1000{\text{kg/m}}^3$
Say, $l=3\text{cm},d=2\text{cm}$
Pressure at $A$ and $B$ will be same.
$\therefore P_o+{\rho }_{o}g(l+d))=P_o+{\rho }_{w}gd$
($P_o=$ atmospheric pressure)
$\Rightarrow {\rho }_0(0.03+0.02)=1000\times 0.02$
$\therefore$ Density of oil, ${\rho }_o=400{\text{kg/m}}^3$