A) \[\frac{x({{\mu }_{1}}+{{\mu }_{2}})}{2{{\mu }_{1}}{{\mu }_{2}}}\]
B) \[\frac{x\,{{\mu }_{1}}\,{{\mu }_{2}}}{2({{\mu }_{1}}+{{\mu }_{2}})}\]
C) \[\frac{x{{\mu }_{1}}{{\mu }_{2}}}{({{\mu }_{1}}+{{\mu }_{2}})}\]
D) \[\frac{2x({{\mu }_{1}}+{{\mu }_{2}})}{{{\mu }_{1}}{{\mu }_{2}}}\]
E) \[\frac{4({{\mu }_{1}}+{{\mu }_{2}})x}{{{\mu }_{1}}{{\mu }_{2}}}\]
Correct Answer: A
Solution :
Apparent depth \[=\frac{\text{Real}\,\text{depth}}{\mu }\] For oil apparent depth\[=\frac{x}{2{{\mu }_{1}}}\] and for water apparent depth\[=\frac{x}{2{{\mu }_{2}}}\] The apparent depth of the vessel \[=\frac{x}{2{{\mu }_{1}}}+\frac{x}{2{{\mu }_{2}}}\] \[=\frac{x}{2}\left[ \frac{1}{{{\mu }_{1}}}+\frac{1}{{{\mu }_{2}}} \right]=\frac{x}{2}\left[ \frac{{{\mu }_{1}}+{{\mu }_{2}}}{{{\mu }_{1}}{{\mu }_{2}}} \right]\]
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