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 gravity of alloy \[=\frac{Density of alloy}{\text{Density of water}}\] \[=\frac{\text{Mass of alloy }}{\text{Volume of alloy}\times \text{density of water }}\] \[=\frac{{{m}_{1}}+{{m}_{2}}}{\left( \frac{{{m}_{1}}}{{{\rho }_{1}}}+\frac{{{m}_{2}}}{{{\rho }_{2}}} \right)\times {{\rho }_{w}}}\]\[=\frac{{{m}_{1}}+{{m}_{2}}}{\frac{{{m}_{1}}}{{{\rho }_{1}}/{{\rho }_{w}}}+\frac{{{m}_{2}}}{{{\rho }_{2}}/{{\rho }_{w}}}}=\frac{{{m}_{1}}+{{m}_{2}}}{\frac{{{m}_{1}}}{{{s}_{1}}}+\frac{{{m}_{2}}}{{{s}_{2}}}}\] \[\left[ \text{As specific gravity of substance }=\frac{\text{density of substance }}{\text{density of water}} \right]\]
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