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Chapter 1: Problem 19

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

Short Answer

Expert verified
1) \(1000\mathrm{~g} \mathrm{~m}^{-3}\) 2) \(\dfrac{1}{1000} \mathrm{~g} \mathrm{~cm}^{-3}\) 3) \(1 \mathrm{~kg} \mathrm{~cm}^{-3}\) Answer: 1) \(1000\mathrm{~g} \mathrm{~m}^{-3}\) and 2) \(\dfrac{1}{1000} \mathrm{~g} \mathrm{~cm}^{-3}\)

Step by step solution

01

Rewrite the given density with conversion factors

First, you need to rewrite the quantity with the conversion factors. To convert from kilograms to grams, you can use the conversion factor of \(1 \mathrm{~kg}=1000\mathrm{~g}\), and to convert from meters to centimeters, you can use the conversion factor of \(1\mathrm{~m} = 100\mathrm{~cm}\).
02

Convert the grams to kilograms

Multiply the given density by the conversion factor from kilograms to grams: \((1\mathrm{~kg} \mathrm{~m}^{-3})\times(1000\mathrm{~g}/1\mathrm{~kg}) = 1000\mathrm{~g} \mathrm{~m}^{-3}\). This matches alternative (1).
03

Convert the meters to centimeters

Now, convert the given density from meters to centimeters: \((1\mathrm{~kg} \mathrm{~m}^{-3})\times(100\mathrm{~cm}/1\mathrm{~m})^3 = 1\mathrm{~kg} \left(\frac{100\mathrm{~cm}}{1\mathrm{~m}}\right)^3 \mathrm{cm}^{-3} = 1\mathrm{~kg}~\frac{1}{1~000\,000}~\mathrm{cm}^{-3}\).
04

Convert the kilograms to grams in the result from Step 3

Convert the kilograms to grams in the obtained expression from step 3: \(1\mathrm{~kg}~\frac{1}{1~000\,000}~\mathrm{cm}^{-3}\times\frac{1000\mathrm{~g}}{1\mathrm{~kg}} =\frac{1}{1000} \mathrm{~g} \mathrm{~cm}^{-3}\). This matches alternative (2).
05

Compare the obtained expressions to the alternatives

We have found two expressions: \(1000 \mathrm{~g} \mathrm{~m}^{-3}\) and \(\frac{1}{1000} \mathrm{~g} \mathrm{~cm}^{-3}\). Comparing these expressions to the alternatives, we can see that (1) \(1 \mathrm{~kg}\mathrm{~m}^{-3}=1000 \mathrm{~g} \mathrm{~m}^{-3}\) and (2) \(1 \mathrm{~kg} \mathrm{~m}^{-3}=\frac{1}{1000} \mathrm{~g} \mathrm{~cm}^{-3}\).

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Most popular questions from this chapter

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

An atlas of a country is shown in the figure, the distance between cities \(A\) and \(B\) is _______. (1) \(35 \mathrm{~km}\) (2) \(3500 \mathrm{~m}\) (3) \(350 \mathrm{~km}\) (4) Both (1) and (2)

The mass of a body of weight 200 gf is _____ \(\mathrm{g}\). (1) \(\quad 200\) (2) \(\quad 300\) (3) 400 (4) \(\quad 20\)

What causes the formation of the land and sea breezes?

1 kilogram is equal to _______. (1) 1000 gram (2) 100 gram (3) 1000 milligram (4) 100 milligram
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