Numericals- Relative density

🔬 Relative Density Numericals (with Solutions)

1. Convert density of copper 8.83 g/cm³ to SI unit.

1 g/cm³ = 1000 kg/m³
So, 8.83 g/cm³ = 8.83 × 1000 = 8830 kg/m³

2. R.D. of mercury is 13.6. Find density in CGS & SI.

R.D. = Density of mercury / Density of water
In CGS: Density = 13.6 × 1 = 13.6 g/cm³
In SI: 13.6 × 1000 = 13,600 kg/m³

3. Density of iron = 7.8 × 10³ kg/m³. Find R.D.

R.D. = Density of iron / Density of water
R.D. = (7.8 × 10³) / (1 × 10³) = 7.8

4. R.D. of silver = 10.8. Find density.

Density = R.D. × Density of water
= 10.8 × 1000 = 10,800 kg/m³

5. Volume = 12 cm³, R.D. = 2.5. Find mass.

Density = 2.5 g/cm³
Mass = Density × Volume = 2.5 × 12 = 30 g

6. Room: 4.5 × 3.5 × 2.5 m³. Density of air = 1.3 kg/m³

Volume = 4.5 × 3.5 × 2.5 = 39.375 m³
Mass = 1.3 × 39.375 = 51.19 kg

7. Stone = 113 g. Water rises: 30 ml to 40 ml → Volume = 10 cm³

R.D. = Mass / Volume = 113 / 10 = 11.3

8. Volume = 100 cm³, Weight in air = 1 kg

Volume of water displaced = 100 cm³ = 0.1 L = 0.1 kg
Loss in weight = 0.1 kg ⇒ Weight in water = 1 - 0.1 = 0.9 kg
R.D. = 1 / 0.1 = 10

9. Mass = 70 kg, Volume displaced = 20,000 cm³ = 0.02 m³

Loss in weight = 0.02 × 1000 × 9.8 = 196 N
Actual weight = 70 × 9.8 = 686 N
Apparent weight = 686 - 196 = 490 N
R.D. = 70 / 20 = 3.5

10. Weight in air = 120 gf, water = 40 gf

Loss = 120 - 40 = 80 gf
R.D. = 120 / 80 = 1.5

11. Weight in air = 32 gf, in water = 28.8 gf, Volume = 3 cm³

Loss = 32 - 28.8 = 3.2 gf
Density = Mass / Volume = 32 / 3 = 10.67 g/cm³
R.D. = 10.67 / 1 = 10.67

12. Weight in air = 96 gf, in water = 80 gf

Loss = 96 - 80 = 16 gf
R.D. = 96 / 16 = 6