Fluid Mechanics Viscosity Question 182
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}} $
Show Answer
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] $
BETA
