Chapter 1: Problem 16

5 litre of a liquid weighs \(5 \mathrm{kgf}\). The density of the liquid is ______. (1) \(1 \mathrm{~kg} \mathrm{~m}^{-3}\) (2) \(1 \mathrm{~g} \mathrm{~cm}^{-3}\) (3) \(100 \mathrm{~kg} \mathrm{~m}^{-3}\) (4) \(100 \mathrm{~g} \mathrm{~m}^{-3}\)

Short Answer

Expert verified

Choose from the following options: (1) \(1 \mathrm{~kg} \mathrm{~m}^{-3}\) (2) \(1 \mathrm{~g} \mathrm{~cm}^{-3}\) (3) \(100 \mathrm{~kg} \mathrm{~m}^{-3}\) (4) \(100 \mathrm{~g} \mathrm{~m}^{-3}\) Answer: The correct density of the liquid is (2) \(1 \mathrm{~g} \mathrm{~cm}^{-3}\).

Step by step solution

Write down the given parameters.

We are given: - Weight of the liquid = \(5 \mathrm{kgf}\) - Volume of the liquid = \(5 \mathrm{L}\)

Convert the weight to mass.

We need to convert the given weight (in kgf) to mass (in kg) for the sake of finding density. The conversion factor is 1 kgf = 1 kg. So the mass of the liquid = \(5 \mathrm{kgf} \times \frac{1 \mathrm{kg}}{1 \mathrm{kgf}} = 5 \mathrm{kg}\).

Convert the volume to consistent units.

The options we are given are either in meters or centimeters. To compare with these options, we need to convert the given volume (in liters) to meters cubed (m^3) or cm^3. 1 L = 1000 cm^3 , so the volume of the liquid = \(5 \mathrm{L} \times \frac{1000 \mathrm{cm^3}}{1\mathrm{L}} = 5000 \mathrm{cm^3}\) 1 cm^3 = 0.000001 m^3, so the volume of the liquid = \(5000 \mathrm{cm^3} \times \frac{0.000001 \mathrm{m^3}}{1\mathrm{cm^3}} = 0.005 \mathrm{m^3}\).

Calculate the density.

Now that we have the mass and volume in consistent units, we can calculate the density of the liquid: Density = \(\frac{Mass}{Volume}\) In kg/m^3: Density = \(\frac{5\mathrm{kg}}{0.005\mathrm{m^3}}=1000\mathrm{~kg} \mathrm{~m}^{-3}\) In g/cm^3: First, we convert the mass to grams: 1 kg = 1000 g, so 5 kg = 5000 g. Density = \(\frac{5000\mathrm{g}}{5000\mathrm{cm^3}}=1\mathrm{~g} \mathrm{~cm}^{-3}\)

Compare the calculated density to the options provided.

The calculated densities are: - \(1000 \mathrm{~kg} \mathrm{~m}^{-3}\) in kg/m^3 - \(1 \mathrm{~g} \mathrm{~cm}^{-3}\) in g/cm^3 After comparing the calculated densities to the options provided: (1) \(1 \mathrm{~kg} \mathrm{~m}^{-3}\) (Incorrect) (2) \(1 \mathrm{~g} \mathrm{~cm}^{-3}\) (Correct) (3) \(100 \mathrm{~kg} \mathrm{~m}^{-3}\) (Incorrect) (4) \(100 \mathrm{~g} \mathrm{~m}^{-3}\) (Incorrect) The correct answer is (2) \(1 \mathrm{~g} \mathrm{~cm}^{-3}\).

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5 litre of a liquid weighs \(5 \mathrm{kgf}\). The density of the liquid is ______. (1) \(1 \mathrm{~kg} \mathrm{~m}^{-3}\) (2) \(1 \mathrm{~g} \mathrm{~cm}^{-3}\) (3) \(100 \mathrm{~kg} \mathrm{~m}^{-3}\) (4) \(100 \mathrm{~g} \mathrm{~m}^{-3}\)

Short Answer

Step by step solution

Write down the given parameters.

Convert the weight to mass.

Convert the volume to consistent units.

Calculate the density.

Compare the calculated density to the options provided.

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