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 cm of water in one arm and 12.5 cm of oil in the other, as shown in the figure. What is the relative density of oil?

• A. 0.8
• B. 1.0
• C. 1.2
• D. 1.4

Answer 1

The correct option is A

0.8

Since the level of mercury is at the same height in the two arms, the pressure due to $h_w=10cm$ of water = pressure due to $h_o=12.5cm$ of oil, i.e.
$h_w{\rho }_{w}g=h_0{\rho }_{0}g$
$\therefore$ Relative density of oil $=\frac{{\rho }_0}{{\rho }_w}=\frac{h_w}{h_0}=\frac{10}{12.5}=0.8$
Hence, the correct choice is (a).