Đáp án:

h' = 17,5cm 

Giải thích các bước giải:

Ta có:

$\begin{array}{l}
{p_A} = {p_B} \Leftrightarrow \dfrac{{{P_1}}}{{{S_1}}} + {d_n}.h = \dfrac{{{P_2}}}{{{S_2}}}\\
 \Leftrightarrow \dfrac{{10{m_1}}}{{{S_1}}} + 10.{D_n}.h = \dfrac{{10{m_2}}}{{{S_2}}}\\
 \Leftrightarrow \dfrac{1}{{{S_1}}} + 1000.0,1 = \dfrac{2}{{{S_2}}}\\
 \Leftrightarrow \dfrac{2}{{{S_2}}} - \dfrac{1}{{{S_1}}} = 100\left( 1 \right)\\
{p_M} = {p_N} \Leftrightarrow \dfrac{{{P_1} + P}}{{{S_1}}} = \dfrac{{{P_2}}}{{{S_2}}}\\
 \Leftrightarrow \dfrac{{10{m_1} + 10m}}{{{S_1}}} = \dfrac{{10{m_2}}}{{{S_2}}}\\
 \Leftrightarrow \dfrac{{1 + 2}}{{{S_1}}} = \dfrac{2}{{{S_2}}} \Leftrightarrow \dfrac{3}{{{S_1}}} - \dfrac{2}{{{S_2}}} = 0\left( 2 \right)\\
\left( 1 \right),\left( 2 \right) \Rightarrow \left\{ \begin{array}{l}
\dfrac{1}{{{S_1}}} = 50\\
\dfrac{1}{{{S_2}}} = 75
\end{array} \right.
\end{array}$

Vị trí cân bằng cao hơn là:

$\begin{array}{l}
{p_C} = {p_D} \Leftrightarrow \dfrac{{{P_1}}}{{{S_1}}} + {d_n}.h' = \dfrac{{{P_2} + P}}{{{S_2}}}\\
 \Leftrightarrow  - \dfrac{{10{m_1}}}{{{S_1}}} + \dfrac{{10{m_2} + 10m}}{{{S_2}}} = 10{D_n}.h'\\
 \Leftrightarrow 3.75 - 1.50 = 1000.h'\\
 \Leftrightarrow 175 = 1000h'\\
 \Leftrightarrow h' = 0,175m = 17,5cm
\end{array}$

Vậy lúc này nhánh 1 cao hơn nhánh hai 17,5cm