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

• A. $⟮\frac{m_1+m_2}{s_1+s_2}⟯$
• B. $⟮\frac{s_1{s}_2}{m_1+m_2}⟯$
• C. $\frac{m_1+m_2}{⟮\frac{m_1}{s_1}+\frac{m_2}{s_2}⟯}$
• D. $\frac{⟮\frac{m_1}{s_1}+\frac{m_2}{s_2}⟯}{m_1+m_2}$

Answer 1

The correct option is C

$\frac{m_1+m_2}{⟮\frac{m_1}{s_1}+\frac{m_2}{s_2}⟯}$

Specific gravity of alloy = $\frac{\text{Density of alloy}}{\text{Densityof water}}$

$=\frac{\text{Mass of alloy}}{\text{Volume of alloy}\times \text{density of water}}$

$=\frac{m_1+m_2}{⟮\frac{m_1}{{\rho }_1}+\frac{m_2}{{\rho }_2}⟯\times {\rho }_w}=\frac{m_1+m_2}{\frac{m_1}{{\rho }_1/{\rho }_w}+\frac{m_2}{{\rho }_2/{\rho }_w}}=\frac{m_1+m_2}{\frac{m_1}{s_1}+\frac{m_2}{s_2}}$ $[\text{As specific gravity of substance}=\frac{\text{density of substance}}{\text{density of water}}]$