A bottle weighs $30 g$ when empty, $53.4 g$ when completely filled with a liquid and $48 g$ when completely filled with water. Calculate the density of the liquid. Take, density of water $= 1000 k g / m^{3}$ .

1300 k g / m^{3}

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13 k g / m^{3}

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245 k g / m^{3}

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None of these

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Solution

The correct option is A $1300 k g / m^{3}$
The mass of the bottle is given as 30 g.
The mass of the liquid is given as 53.4 g - 30 g = 23.4 g.
The mass of water is given as 48 g - 30 g = 18 g = 0.018 kg.
The volume is calculated.
We know, Density = Mass / Volume.
As the mass of water is determined and the density of water is given, the volume of water is given as follows.
Volume = Mass / Density = 0.018 / 1000 = $18 \times 10^{- 6} m^{3}$ .
Now the density of the liquid is given as, $\frac{23.4 \times 10^{- 3} m^{3}}{18 \times 10^{- 6} m^{3}} = 1300 k g / m^{3}$ .

Hence, the density of the liquid is $1300 k g / m^{3}$ .

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A bottle weighs 30g when empty, 53.4g when completely filled with a liquid and 48g when completely filled with water. Calculate the density of the liquid. Take, density of water=1000kg/m3.

A bottle weighs $30 g$ when empty, $53.4 g$ when completely filled with a liquid and $48 g$ when completely filled with water. Calculate the density of the liquid. Take, density of water $= 1000 k g / m^{3}$ .