Q. 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) $\left( \frac{m_{1} + m_{2}}{s_{1} + s_{2}} \right)$
B) $\left( \frac{s_{1}s_{2}}{m_{1} + m_{2}} \right)$
C) $\frac{m_{1} + m_{2}}{\frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}}}$
D) $\frac{\frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}}}{m_{1} + m_{2}}$
Explanation
(c) Specific gravity of alloy $= \frac{Density\ of\ alloy}{Density\ of\ water}$
$= \frac{Mass\ of\ alloy}{Volume\ of\ alloy \times density\ of\ water}$
$= \frac{m_{1} + m_{2}}{\left( \frac{m_{1}}{\rho_{1}} + \frac{m_{2}}{\rho_{2}} \right) \times \rho_{w}} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{\rho_{1}/\rho_{w}} + \frac{m_{2}}{\rho_{2}/\rho_{w}}} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}}}$
$\left\lbrack As\ specific\ gravity\ of\ substance = \frac{density\ of\ substance}{density\ of\ water} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.