Question

An open U-tube contains mercury. When $11.2cm$ of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm form its initial level?

• A. 0.56 cm
• B. 1.35 cm
• C. 0.41 cm
• D. 2.32 cm

Answer 1

Answer: (C)

Key Idea : At the same level in the two limbs of a U-tube, pressure is same.
On pouring water on left side, mercury rises $xcm$ (say) from its previous level in the right limb of $U$-tube creating a difference of levels of mercury by $2xcm$. Equating pressures at $A$ and $B$, we get

$P_A=P_B$
$\therefore 11.2\times 10^{-2}\times {\rho }_{\text{water }}\times g=2x\times {\rho }_{\text{mercury }}\times g$
$\Rightarrow 11.2\times 10^{-2}\times 1000kg/m^3$
$=2x\times 13600\times kg/m^3$
$\Rightarrow x=\frac{11.2\times 10^{-2}\times 1000m}{2\times 13600}$
$=0.41cm$