If $M_{1}$ gm of a substance with specific gravity $S_{1}$ is mixed with $M_{2}$ gm of a substance with specific gravity $S_{2}$ and then the substances are used to make an alloy. What will be the specific gravity of the alloy.

\frac{M_{1} + M_{2}}{S_{1} S_{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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\frac{\frac{M_{1}}{S_{1}} + \frac{M_{2}}{S_{2}}}{M_{1} M_{2}}

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Solution

The correct option is B $\frac{M_{1} + M_{2}}{\frac{M_{1}}{S_{1}} + \frac{M_{2}}{S_{2}}}$
A very fundamental property of any substance on this planet is the conservation of mass.

Therefore, if I mix two substances with mass $M_{1} a n d M_{2}$ then there combined mass will always be, $M_{1} + M_{2}$

An additional property in case of fluids is the conservation of volume.

If 2 fluids with volumes $V_{1} a n d V_{2}$ are mixed, the combined volume will be, $V_{1} + V_{2}$

Here,

$V_{1} = \frac{M_{1}}{S_{1}}$ and $V_{2} = \frac{M_{2}}{S_{2}}$

Therefore, total volume on mixing = $\frac{M_{1}}{S_{1}} + \frac{M_{2}}{S_{2}}$

Hence, the specific gravity of the new alloy will be total mass/total volume

$S^{'} = \frac{M_{1} + M_{2}}{\frac{M_{1}}{S_{1}} + \frac{M_{2}}{S_{2}}}$

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If M1 gm of a substance with specific gravity S1 is mixed with M2 gm of a substance with specific gravity S2 and then the substances are used to make an alloy. What will be the specific gravity of the alloy.

If $M_{1}$ gm of a substance with specific gravity $S_{1}$ is mixed with $M_{2}$ gm of a substance with specific gravity $S_{2}$ and then the substances are used to make an alloy. What will be the specific gravity of the alloy.