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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
$\left( {\frac{{{m_1} + {m_2}}}{{{s_1} + {s_2}}}} \right)$
$\left( {\frac{{{s_1}{s_2}}}{{{m_1} + {m_2}}}} \right)$
$\left[ {\frac{{{m_1} + {m_2}}}{{({m_1}/{s_1}\, + \,{m_2}/{s_2})}}} \right]$
$\left[ {\frac{{({m_1}/{s_1}\, + \,{m_2}/{s_2})}}{{{m_1} + {m_2}}}} \right]$
Solution
Specific gravity of alloy
$=\frac{\text { mass of alloy }}{\text { volume of alloy }} \times$ $density\,\, of\,\, water$
$\mathrm{s}_{\text {alloy }}=\frac{\mathrm{m}_{1}+\mathrm{m}_{2}}{\left(\frac{\mathrm{m}_{1}}{\mathrm{d}_{1}}+\frac{\mathrm{m}_{2}}{\mathrm{d}_{2}}\right) \times \mathrm{d}_{\mathrm{w}}}$
$=\frac{m_{1}+m_{2}}{\left[\frac{m_{1}}{\left(d_{1} / d_{w}\right)}+\frac{m_{2}}{\left(d_{2} / d_{w}\right)}\right]}=\frac{m_{1}+m_{2}}{\left(\frac{m_{1}}{s_{1}}+\frac{m_{2}}{s_{2}}\right)}$