A) \[{{D}_{A}}={{\left[ {{D}_{B}}\cdot \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right]}^{1/2}}\]
B) \[{{D}_{A}}={{\left[ {{D}_{B}}\cdot \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right]}^{1/2}}\]
C) \[{{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right)}^{1/2}}\]
D) \[{{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right)}^{1/2}}\]
Correct Answer: D
Solution :
\[\frac{{{D}_{A}}}{{{D}_{B}}}=\sqrt{\frac{{{\rho }_{B}}}{{{\rho }_{A}}}}={{\left[ \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right]}^{\frac{1}{2}}}\]; \[\therefore {{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right)}^{\frac{1}{2}}}\]
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