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

$⟮ \frac{m_{1} + m_{2}}{s_{1} + s_{2}} ⟯$

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$⟮ \frac{s_{1} s_{2}}{m_{1} + m_{2}} ⟯$

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$\frac{m_{1} + m_{2}}{⟮ \frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}} ⟯}$

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$\frac{⟮ \frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}} ⟯}{m_{1} + m_{2}}$

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Solution

The correct option is C
$\frac{m_{1} + m_{2}}{⟮ \frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}} ⟯}$

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

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

$= \frac{m_{1} + m_{2}}{⟮ \frac{m_{1}}{ρ_{1}} + \frac{m_{2}}{ρ_{2}} ⟯ \times ρ_{w}} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{ρ_{1} / ρ_{w}} + \frac{m_{2}}{ρ_{2} / ρ_{w}}} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}}}$ $[As specific gravity of substance = \frac{density of substance}{density of water}]$

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In making an alloy, a substance of specific gravity s1 and mass m1 is mixed with another substance of specific gravity s2 and mass m2; then the specific gravity of the alloy is

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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