Density of the material of a paper is given as \(0.5 \mathrm{~g} \mathrm{~cm}^{-3}\). The mass of the paper is \(1 \mathrm{~g}\) and its length and breadth are \(10 \mathrm{~cm}\) and \(5 \mathrm{~cm}\) respectively. Arrange the following steps in a sequence to find the thickness of the paper. (a) The thickness of the paper is \(=\frac{\text { volume }(\mathrm{V}) \text { of the paper }}{\text { length } \times \text { breadth }}\) (b) The density (d) of the material of the paper is \(=\frac{\text { mass of the paper(m) }}{\text { volume of the paper(V) }}\) (c) Then the volume \((\mathrm{V})\) of the paper \(=\frac{\text { mass of the paper }(\mathrm{m})}{\text { density }(\mathrm{d}) \text { of the paper }}\) (d) The volume \((\mathrm{V})\) of the paper is \(=\) length \(\times\) breadth \(\times\) thickness of the paper. (1) abcd (2) badc (3) \(\mathrm{abdc}\) (4) \(\mathrm{bcda}\)

Step by step solution

01

Use the density formula to find the volume of the paper

The formula for the density of a material is given as: Density (d) = (mass of the paper (m)) / (volume of the paper (V)). We are given the density (d = 0.5 g/cm³) and the mass of the paper (m = 1 g). Using this, we can find the volume of the paper (V): Volume (V) = (mass of the paper (m)) / (density of the paper (d))

02

Calculate the volume of the paper

Now, we will plug in the values of mass (m = 1 g) and density (d = 0.5 g/cm³) to find the volume of the paper: Volume (V) = \(\frac{1\mathrm{~g}}{0.5\mathrm{~g/cm}^3}\) = 2 cm³

03

Determine the formula to find the thickness of the paper

We can find the thickness of the paper by dividing the volume of the paper (V) by the product of its length and breadth. The formula is: Thickness of the paper = \(\frac{\text{ volume }(\mathrm{V}) \text{ of the paper }}{\text { length } \times \text { breadth }}\)

04

Calculate the thickness of the paper

Using the formula from Step 3, we will plug in the values for volume (V = 2 cm³), length (10 cm) and breadth (5 cm) to find the thickness of the paper: Thickness of the paper = \(\frac{2\mathrm{~cm}^3}{10\mathrm{~cm}\times 5\mathrm{~cm}}\) = \(\frac{2}{50}\) = 0.04 cm The correct arrangement of steps for this problem is (c), (d), (a), and therefore the answer is option (4): \(\mathrm{bcda}\).

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