Question

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

• A. $0.56\,cm$
• B. $1.35\,cm$
• C. $0.41\,cm$
• D. $2.32\,cm$

Answer 1

Answer: (C)

$0.41\,cm$

Answer 2

On pouring water on left side, mercury rises $x$ $cm$ (say) from its previous level in the right limb of U-tube creating a difference of levels of mercury by $2 \,x cm$. Equating pressure at $A$ and $B,$ we get

$P_{A}=P_{B}$
$\therefore 11.2 \times 10^{-2} \times \rho_{\text {water }} \times g=2 x \times \rho_{ Hg } \times g$
$11.2 \times 10^{-2} \times 1000 \,kg / m ^{3}$
$=2 x \times 13600 \,kg / m ^{3}$
$x =\frac{11.2 \times 10^{-2} \times 1000}{2 \times 13600} m$
$=0.41 \,cm$