First slide

Pressure in a fluid-mechanical properties of fluids

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

Moderate

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

$\frac{(\frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}})}{m_{1} + m_{2}}$

Solution

Specific gravity of alloy $= \frac{Density of alloy}{Density of water}$
$= \frac{Mass of alloy}{Volume of alloy \times density of water}$
$= \frac{m_{1} + m_{2}}{(\frac{m_{1}}{ρ_{1}} + \frac{m_{2}}{ρ_{2}}) \times ρ_{w}} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{ρ_{1} / ρ_{w}} + \frac{m_{2}}{ρ_{2} / ρ_{w}}} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}}}$
$[As specific gravity of substance = \frac{density of substance}{density of water}]$

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