A) \[\rho =\frac{{{\rho }_{1}}+{{\rho }_{2}}}{2}\]
B) \[\rho =\frac{{{\rho }_{1}}+{{\rho }_{2}}}{2{{\rho }_{1}}{{\rho }_{2}}}\]
C) \[\rho =\frac{2{{\rho }_{1}}{{\rho }_{2}}}{{{\rho }_{1}}+{{\rho }_{2}}}\]
D) \[\rho =\frac{{{\rho }_{1}}{{\rho }_{2}}}{{{\rho }_{1}}+{{\rho }_{2}}}\]
Correct Answer: C
Solution :
\[\rho =\frac{\text{Total mass}}{\text{Total volume }}=\frac{2m}{{{V}_{1}}+{{V}_{2}}}=\frac{2m}{m\,\left( \frac{1}{{{\rho }_{1}}}+\frac{1}{{{\rho }_{2}}} \right)}\] \\[\rho =\frac{2{{\rho }_{1}}{{\rho }_{2}}}{{{\rho }_{1}}+{{\rho }_{2}}}\]
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