A) \[n={{n}_{1}}+{{n}_{2}}+{{n}_{3}}\]
B) \[\frac{1}{n}=\frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}\]
C) \[\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{{{n}_{1}}}}+\frac{1}{\sqrt{{{n}_{2}}}}+\frac{1}{\sqrt{{{n}_{3}}}}\]
D) \[\frac{1}{{{n}^{1}}}=\frac{1}{n_{1}^{2}}+\frac{1}{n_{2}^{2}}+\frac{1}{n_{3}^{2}}\]
Correct Answer: B
Solution :
\[n=\frac{1}{2l}\sqrt{\frac{T}{m}}\]Þ \[{{n}_{1}}{{l}_{1}}={{n}_{2}}{{l}_{2}}={{n}_{3}}{{l}_{3}}=k\] \[{{l}_{1}}+{{l}_{2}}+{{l}_{3}}=l\]Þ\[\frac{k}{{{n}_{1}}}+\frac{k}{{{n}_{2}}}+\frac{k}{{{n}_{3}}}=\frac{k}{n}\] Þ \[\frac{1}{n}=\frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}+........\]
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