Question

The same physical quantity, such as density, can be reported using different units. Above, you found that water has a density of 1000kg/m3=1g/cm3 . Because the density of water must be the same regardless of what units you use to measure it, you can conclude that an object whose density is 1 kg/m3 must be less dense than water. In other words, 1 kg/m3 is less than 1 g/cm3 . If you had three different objects with densities of 1 kg/m3 , 1 g/m3 , and 1 kg/mm3 , which object would be the most dense? Rank the given densities from most to least dense. To rank items as equivalent, overlap them.

Answer 1

In the question there are three values of densities.

We are asked to arrange these values in descending order.

In order to solve this problem first we have to convert each values into same unit.Let the unit chosen to be gram per cubic centimeter.

The first value is 1000 kg per cubic metre.

we know that 1 kg=1000 kg and and 1 m=100 cm

Hence the value in CGS system will be-

`1 kg/m^3 =(10^3 gram)/([10^2cm]^3)`

`=10^-3\ g/cm^3`

The second value is 1 gram per cubic centimetre.

Third value is 1 kg per cubic millimeter.

we know that

`1 mm =10^-1 cm`

Hence 1 kg per cubic millimeter i.e

`1 kg/mm^3`

`=(10^3 gram)/([10^-1cm]^3)`

`=10^6 g/cm^3`

Hence the perfect order will be-

`10^6 g/cm^3` >
`1 g/cm^3` >
`10^-3\ g/cm^3`

`i.e\ 1 kg/mm^3>1\ g/cm^3>1 kg/m^3`

Answer 2

1 kg/mm³, 1 kg/m³, 1 g/m³

Step-by-step explanation:

We have 3 objects of different densities, 1 kg/m³, 1 g/m³, and 1 kg/mm³.

In order to compare their densities, we will express all of them in the same units, for instance, kg/m³.

First object

It has a density of 1 kg/m³.

Second object

We know that 1 kg = 10³ g. Then,

1 g/m³ × (1 kg/10³ g) = 10⁻³ kg/m³

Third object

We know that 1 m = 10³ mm. Then,

1 kg/mm³ × (10³ mm/1 m)³ = 10⁹ kg/mm³

The densities, from most to least dense are:

1 kg/mm³, 1 kg/m³, 1 g/m³