Density – Step-by-Step Numerical Problems (Class 8 Physics) – Part 3 (Advanced Problems)

Title : Density Numerical Problems with Step-by-Step Solution / Class 8
Physics – Part 3

Question: 9

The mass of an empty density bottle is 21.8 g.When filled completely with water, it is
41.8 g and When filled completely with liquid, it is 40.6 g.

Find:

(a) Volume of the density bottle

(b) Relative density of the liquid

Solution:

Given:

Mass of empty bottle, m₁ = 21.8 g
Mass of bottle + water, m₂ = 41.8 g
Mass of bottle + liquid, m₃ = 40.6 g

(a) Volume of the density bottle

Step 1: Mass of water

Mass of water = m₂ − m₁
= 41.8 g − 21.8 g
= 20 g

Step 2: Volume of density bottle

Density of water = 1 g/cm³
Mass of water = 20 g

Formula:

Volume = Mass / Density

Substitution:

, Volume = 20 g / 1 g/cm³
Volume = 20 cm³

Since,

1 mL = 1 cm³
Volume = 20 mL

Final Answer (a): Volume of density bottle = 20 mL

(b) Find the relative density of the liquid

Step 1: Mass of liquid

Mass of liquid = m₃ − m₁
= 40.6 g − 21.8 g
= 18.8 g

Step 2: Volume of liquid

Volume of liquid = Volume of bottle
V = 20 cm³

Step 3: Formula

Density = Mass / Volume

Step 4: Substitution

Density = 18.8 g / 20 cm³
Density = 0.94 g/cm³

Step 5: Relative Density

Formula:

Relative density = Density of liquid / Density of water

Density of water = 1 g/cm³