Đáp án:
$\begin{array}{l}
a.{m_1} = {m_2} = 2kg\\
b.h = 10cm
\end{array}$
Giải thích các bước giải:
a. Khối lượng các pit tông là:
$\begin{array}{l}
{p_A} = {p_B} \Leftrightarrow \dfrac{{{P_1} + P}}{{{S_1}}} = \dfrac{{{P_2}}}{{{S_2}}} + {d_n}.{h_1}\\
\Leftrightarrow \dfrac{{10{m_1} + 10m}}{{{S_1}}} = \dfrac{{10{m_2}}}{{{S_2}}} + 10{D_n}.{h_1}\\
\Leftrightarrow \dfrac{{{m_1} + 1}}{{1,5{S_2}}} - \dfrac{{{m_1}}}{{{S_2}}} = 1000.0,2\\
\Leftrightarrow \dfrac{{{m_1} + 1 - 1,5{m_1}}}{{1,5{S_2}}} = 200\\
\Leftrightarrow 300{S_2} - 0,5{m_1} = 1\left( 1 \right)\\
{p_C} = {p_D} \Leftrightarrow \dfrac{{{P_2} + P}}{{{S_2}}} = \dfrac{{{P_1}}}{{{S_1}}} + {d_n}.{h_2}\\
\Leftrightarrow \dfrac{{10{m_2} + 10m}}{{{S_2}}} = \dfrac{{10{m_1}}}{{{S_1}}} + 10{D_n}.{h_2}\\
\Leftrightarrow \dfrac{{{m_1} + 1}}{{{S_2}}} - \dfrac{{{m_1}}}{{1,5{S_2}}} = 1000.0,05\\
\Leftrightarrow \dfrac{{1,5{m_1} + 1,5 - {m_1}}}{{1,5{S_2}}} = 50\\
\Leftrightarrow 75{S_2} + 0,5{m_1} = 1,5\left( 2 \right)\\
\left( 1 \right),\left( 2 \right) \Rightarrow \left\{ \begin{array}{l}
{m_1} = {m_2} = 2kg\\
{S_2} = \dfrac{1}{{150}}{m^2}
\end{array} \right.
\end{array}$
b. Độ chênh lệch khi không bỏ quả cân là:
$\begin{array}{l}
{p_M} = {p_N} \Leftrightarrow \dfrac{{{P_1}}}{{{S_1}}} = \dfrac{{{P_2}}}{{{S_2}}} + {d_n}.h\\
\Leftrightarrow \dfrac{{10{m_1}}}{{{S_1}}} = \dfrac{{10{m_2}}}{{1,5{S_1}}} + 10.{D_n}.h\\
\Leftrightarrow \dfrac{2}{{\dfrac{1}{{150}}}} = \dfrac{2}{{\dfrac{{1,5}}{{150}}}} + 1000h\\
\Leftrightarrow 1000h = 200 \Rightarrow h = 0,1m = 10cm
\end{array}$
