Question

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​

Answer 1

Specific gravity of an alloy is $= \bf{\frac { (m1+m2) } { ( \frac{m1}{s_1} + \frac{m2}{s_2})}}$

Explanation:

The density of an alloy or a material =  Total mass of an alloy / Total volume of an alloy, given by

$\rho = \frac{m}{v}$

Total mass of an alloy = m1 + m2

Total volume of an alloy =  $\frac{m1}{\rho1} + \frac{m2}{\rho2}$

Density of water = $\rho_w$

Specific gravity of an alloy =density of an alloy / density of water

= (total mass of an alloy / total volume of an alloy) / density of water

$= \frac { (m1+m2)/ ( \frac{m1}{\rho1} + \frac{m2}{\rho2})}{\rho_w}$

$= \frac { (m1+m2) } { ( \frac{m1}{\rho1} + \frac{m2}{\rho2})\rho_w}}$

$= \frac{(m1+m2)}{ \frac{m1} {\rho_1 / \rho_w } + \frac{m2} {\rho_1 / \rho_w }}$

$= \frac { (m1+m2) } { ( \frac{m1}{s_1} + \frac{m2}{s_2})}$

Thus,  Specific gravity of an alloy is $= \bf{\frac { (m1+m2) } { ( \frac{m1}{s_1} + \frac{m2}{s_2})}}$