A) \[\left( \frac{{{m}_{1}}+{{m}_{2}}}{{{s}_{1}}+{{s}_{2}}} \right)\]
B) \[\left( \frac{{{s}_{1}}{{s}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)\]
C) \[\frac{{{m}_{1}}+{{m}_{2}}}{\left( \frac{{{m}_{1}}}{{{s}_{1}}}+\frac{{{m}_{2}}}{{{s}_{2}}} \right)}\]
D) \[\frac{\left( \frac{{{m}_{1}}}{{{s}_{1}}}+\frac{{{m}_{2}}}{{{s}_{2}}} \right)}{{{m}_{1}}+{{m}_{2}}}\]
Correct Answer: C
Solution :
\[Specific\text{ }gravity\text{ }of\text{ }alloy=\frac{Density\,of\,alloy}{Density\,of\,water}\] \[=\,\,\,\,\,\frac{Mass\,\,of\,\,alloy}{Volume\,of\,alloy\times density\,of\,water}\] \[=\,\,\,\,\frac{{{m}_{1}}+{{m}_{2}}}{\left( \frac{{{m}_{1}}}{{{\rho }_{1}}}+\frac{{{m}_{2}}}{{{\rho }_{2}}} \right)\times {{\rho }_{w}}}=\frac{{{m}_{1}}+{{m}_{2}}}{\frac{{{m}_{1}}}{{{\rho }_{1}}/{{\rho }_{w}}}+\frac{{{m}_{2}}}{{{\rho }_{2}}/{{\rho }_{w}}}}\] \[=\,\,\,\frac{{{m}_{1}}+{{m}_{2}}}{\frac{{{m}_{1}}}{{{s}_{1}}}+\frac{{{m}_{2}}}{{{s}_{2}}}}\] \[\left[ \begin{align} & As\text{ }specific\text{ }gravity\text{ }of\text{ }substance= \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{density\,\,of\,\,subs\tan ce}{density\,\,of\,\,water} \\ \end{align} \right]\]
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