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Chapter 1: Problem 34

Express the density \(2 \mathrm{~g} \mathrm{~cm}^{-3}\) in SI system.

Short Answer

Expert verified
Question: Convert the given density of 2 g/cm³ into the SI system of units (kg/m³). Answer: The density in SI units is 2000 kg/m³.

Step by step solution

01

Convert grams to kilograms

First, let's convert the mass from grams (g) to kilograms (kg). We know that 1 kg is equal to 1000 g. Therefore, we can divide the given mass by 1000 to get the mass in kilograms: $$ 2 \,\text{g} = \frac{2}{1000} \,\text{kg} $$
02

Convert cubic centimeters to cubic meters

Next, we need to convert the volume unit from cubic centimeters (cm³) to cubic meters (m³). We know that there are 100 cm in 1 m, so we need to multiply the given volume unit by \((100)^3\) to get the volume in cubic meters: $$ 1 \,\text{cm}^3 = \frac{1}{(100)^3} \,\text{m}^3 $$
03

Calculate the density in SI units

Now that we have the mass and volume units in SI units (kg and m³), we can calculate the density in kilograms per cubic meter (kg/m³). $$ \text{Density} = \frac{\text{Mass in kg}}{\text{Volume in m}^3} = \frac{2\times(1/1000)}{1\times(1/(100)^3)} \,\text{kg/m}^3 $$
04

Simplify the equation

To get the final density in SI units, we can simplify the equation as follows: $$ \text{Density} = \frac{2\times(1/1000)}{1\times(1/(100)^3)} = \frac{2}{(1/1000)(1/(100)^3)} = \frac{2}{(1/1000)(1/1000000)} = \frac{2\times1000000}{1/1000} = 2\times1000\times1000 = 2000\,\text{kg/m}^3 $$ The density in SI units is \(2000 \,\text{kg/m}^3\).

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Most popular questions from this chapter

What is a density bottle? Explain how it is used to determine the density of a liquid.

\(1 \mathrm{~kg} \mathrm{~m}^{-3}=\) ________ (1) \(1000 \mathrm{~g} \mathrm{~m}^{-3}\) (2) \(\frac{1}{1000} \mathrm{~g} \mathrm{~cm}^{-3}\) (3) \(10000 \mathrm{~kg} \mathrm{~cm}^{-3}\) (4) \(1 \mathrm{~g} \mathrm{~cm}^{-3}\)

Which of the following statements is/are incorrect? (1) The weight of a body can be zero. (2) The weight of a body can be greater than zero. (3) The mass of a body can be zero. (4) Both (1) and (3)

Mass is measured by using a _______. (1) spring balance (2) physical balance (3) measuring jar (4) metre scale

The distance between two cities \(A\) and \(B\) in a map is \(7.5 \mathrm{~cm}\). The scale taken for drawing this map is \(1 \mathrm{~cm}=1,50,000 \mathrm{~m}\). The actual distance between \(\mathrm{A}\) and \(\mathrm{B}\) is _______ \(\mathrm{km}\). (1) 1125000 (2) \(\quad 20000\) (3) \(\quad 200\) (4) 1125
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