How is the density of a liquid measured with the help of a density bottle?

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Solution

The density bootle used to measure the density of a liquid makes use of the weight of the empty bottle, then the bottle filled with the water and lastly the bottle is weighed with the liquid whose density is to be determined.

Consider that,
The weight of empty bottle = $M_{1} g$
Weight of bottle when water is filled = $M_{2} g$
Weight of bottle when the liquid is filled = $M_{3} g$

The weight of the liquid present in the bottle is:
= $(M_{3} - M_{1}) g$

Whereas the weight of Water
= $(M_{2} - M_{1}) g$

We know that, the volume of $1 g$ of pure water = $1 c m^{3}$

Volume of liquid present in bottle will be same as the volume of water present in the bottle.
= $(M_{2} - M_{1}) c m^{3}$

$∴$ Density of Liquid = $\frac{M a s s o f l i q u i d}{V o l u m e o f l i q u i d} = \frac{(M_{3} - M_{1}) g}{(M_{2} - M_{1}) c m^{3}}$

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