Question

There are three different liquids (liquid 1, liquid 2 and liquid 3) having density 13.6 gm/cc., 1.3 gm/cc and 0.8 gm/cc. Liquid 1 is poured in a uniform U-tube, which is kept vertical. Liquid 2 & liquid 3 are poured separately into the two arms till upper surface of liquid 2 & 3 are same. What is the height of liquid 3 if the height of liquid 2 is 16cm?

• A. 14.4 cm
• B. 16 cm
• C. 15.4 cm
• D. 12.3 cm

Answer 1

The correct option is C

15.4 cm

Pressure at A = Pressure at B

$\Rightarrow$ ${\rho }_3$gh + ${\rho }_1$g(H - h) = ${\rho }_2$gH

$\Rightarrow$ ${\rho }_3$gh - ${\rho }_1$gh = ${\rho }_2$gH - ${\rho }_1$gH

$\Rightarrow$ h(${\rho }_3-{\rho }_1$) = H(${\rho }_2-{\rho }_1$)

$\Rightarrow$ h = $\frac{({\rho }_2-{\rho }_1)}{({\rho }_3-{\rho }_1)}$H = $\frac{({\rho }_1-{\rho }_2)}{({\rho }_1-{\rho }_3)}H$

= 15.4 cm