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 $m_{2}$. The specific gravity of the alloy is

• A. $\frac{m_{1}+m_{2}}{\frac{m_{1}}{s_{1}}+\frac{m_{2}}{s_{2}}}$
• B. $ \frac{m_{1}+m_{2}}{s_{1}+s_{2}}$
• C. $\frac{s_{1} s_{2}}{m_{1}+m_{2}}$
• D. $\frac{\frac{m_{1}}{s_{1}}+\frac{m_{2}}{s_{2}}}{m_{1}+m_{2}}$

Answer 1

Answer: (A)

$V_{1}=\frac{m_{1}}{s_{1} \cdot \rho_{ H _{2} O }}, V_{2}=\frac{m_{2}}{s_{2} \cdot \rho_{ H _{2} O }}$
Sp. gravity of alloy $=\left(\frac{m_{1}+m_{2}}{V_{1}+V_{2}}\right) \div \rho_{ H _{2} C }$
$=\frac{\left(m_{1}+m_{2}\right) \cdot \rho_{ H _{2} O }}{\left(\frac{m_{1}}{s_{1}}+\frac{m_{2}}{s_{2}}\right) \cdot \rho_{ H _{2} O }}=\frac{m_{1}+m_{2}}{\left(\frac{m_{1}}{s_{1}}+\frac{m_{2}}{s_{2}}\right)}$.