A) \[-\frac{1}{{{m}^{2}}}\]
B) \[{{m}^{2}}\]
C) \[-m\]
D) \[\frac{1}{m}\]
Correct Answer: A
Solution :
\[\frac{1}{u}+\frac{1}{v}=\frac{1}{f}\] \[-\frac{1}{{{u}^{2}}}\frac{du}{dt}-\frac{1}{{{v}^{2}}}\frac{dv}{dt}=0\] \[=-\frac{1}{{{u}^{2}}}{{u}_{0}}-\frac{1}{{{v}^{2}}}{{v}_{0}}=0\] \[\frac{{{u}_{0}}}{{{v}_{0}}}=-\frac{{{u}^{2}}}{{{v}^{2}}}=-\frac{1}{{{m}^{2}}}\]
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