Properties Of Solids And Liquids Question 264
Question: In making an alloy, a substance of specific gravity $ s _{1} $ and mass $ m _{1} $ is mixed with another substance of specific gravity $ s _{2} $ and mass $ m _{2} $ ; then the specific gravity of the alloy is [CPMT 1995]
Options:
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}} $
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Answer:
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] $
