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Density

In making an ...

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

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Solution

The correct option is C

$s p e c i f i c g r a v i t y o f a l l o y = \frac{D e n s i t y o f a l l o y}{D e n s i t y o f w a t e r} = \frac{M a s s o f a l l o y}{V o l u m e o f a l l o y \times d e n s i t y o f w a t e r} = \frac{m_{1} + m_{2}}{(\frac{m_{1}}{p_{1}} + \frac{m_{2}}{p_{2}}) \times p_{w}} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{\frac{p_{1}}{p_{w}}} + \frac{m_{2}}{\frac{p_{2}}{p_{w}}}} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{s_{1}} + \frac{m_{2}}{s_{2}}} [A s s p e c i f i c g r a v i t y o f s u b s t a n c e = \frac{d e n s i t y o f s u b s t a n c e}{d e n s i t y o f w a t e r}]$

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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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