Đáp án:

\({l_n} = 2,33{l_d}\)

Giải thích các bước giải:

Ta có:

\(\dfrac{{{S_n}}}{{{S_d}}} = \dfrac{{\dfrac{{{V_n}}}{{{l_n}}}}}{{\dfrac{{{V_d}}}{{{l_d}}}}} = \dfrac{{{l_d}{V_n}}}{{{l_n}{V_s}}} = \dfrac{{{l_d}\dfrac{m}{{{D_n}}}}}{{{l_n}\dfrac{m}{{{D_d}}}}} = \dfrac{{{l_d}{D_d}}}{{{l_n}{D_n}}} = \dfrac{{{l_d}.8900}}{{{l_n}.2700}} = \dfrac{{89{l_2}}}{{27{l_1}}}\)

Ta có:

\(\begin{array}{l}
{R_n} = {R_d}\\
 \Rightarrow {\rho _n}\dfrac{{{l_n}}}{{{S_n}}} = {\rho _d}\dfrac{{{l_d}}}{{{S_d}}}\\
 \Rightarrow \dfrac{{{l_n}}}{{{l_d}}} = \dfrac{{{p_d}{S_n}}}{{{p_n}{S_d}}} = \dfrac{{89{l_d}}}{{27{l_n}}}.\dfrac{{1,{{7.10}^{ - 8}}}}{{2,{{8.10}^{ - 8}}}}\\
 \Rightarrow \dfrac{{{l_n}^2}}{{{l_d}^2}} = 5,4292\\
 \Rightarrow \dfrac{{{l_n}}}{{{l_d}}} = 2,33\\
 \Rightarrow {l_n} = 2,33{l_d}
\end{array}\)