Question

1. Rank the following in terms of increasing density:

A. A100 g object with a volume of 25 cubic centimeters
B. A 200 g object with a volume of 100 cubic centimeters
C. A 100 g object with a volume of 100 cubic centimeters
D. A 400 g object with a volume of 50 cubic centimeters

Answer 1

The density of the objects in increasing order is given as C B A D.

Step-by-step explanation:

Density is the property of mater which compares amount of mater of an object and volume of an object.

The density is given by the formula:

`\rho=(m)/(V)`

Where,

‘ρ’ is density

‘m’ is mass of an object

‘V’ is volume of an object

Object A:

Take object A of 100 g object with a volume of 25 cubic centimetres:

We know that,
`m_(A)=100 \ \mathrm{g}` and
`V_(A)=25 \ \mathrm{cm}^(3)`

Density of A is:

`\Rightarrow \rho_(A)=(m_(A))/(V_(A))`

`\Rightarrow \rho_(A)=(100)/(25)`

`\therefore \rho_(A)=4 \ g / \mathrm{cm}^(3)`

Object B:

Take object A 200 g object with a volume of 100 cubic centimetres:

We know that,
`m_(B)=200 \ \mathrm{g}` and
`V_(B)=100 \ \mathrm{cm}^(3)`

Density of B is:

`\Rightarrow \rho_(B)=(m_(B))/(V_(B))`

`\Rightarrow \rho_(B)=(200)/(100)`

`\therefore \rho_(B)=2 \ g / \mathrm{cm}^(3)`

Object C:

Take object A 100 g object with a volume of 100 cubic centimetres:

We know that,
`m_(C)=100 \ \mathrm{g}` and
`V_(C)=100 \ \mathrm{cm}^(3)`

Density of C is:

`\Rightarrow \rho_(C)=(m_(C))/(V_(C))`

`\Rightarrow \rho_(C)=(100)/(100)`

`\therefore \rho_(C)=1 \ \mathrm{g} / \mathrm{cm}^(3)`

Object D:

Take object A 400 g object with a volume of 50 cubic centimetres:

We know that,
`m_(D)=400 \ \mathrm{g}` and
`V_(D)=50 \ \mathrm{cm}^(3)`

Density of object D is:

`\Rightarrow \rho_(D)=(m_(D))/(V_(D))`

`\Rightarrow \rho_(D)=(400)/(50)`

`\therefore \rho_(D)=8 \ \mathrm{g} / \mathrm{cm}^(3)`

From the above calculation, on comparing,

`C<B<A<D`

Answer 2

C < B < A < D

Step-by-step explanation:

Density is defined as the quotient of Mass divided by Volume, therefore we need to find that quotient for each case in order to rank them:

Case A:
`D = (100)/(25) = 4 (g)/(cm^3)`

Case B:
`D = (200)/(100) = 2 (g)/(cm^3)`

Case C:
`D = (100)/(100) = 1 (g)/(cm^3)`

Case D:
`D = (400)/(50) = 8 (g)/(cm^3)`

So the ranking in INCREASING density is:

C < B < A < D