Numericals . ,Class 8 , ch 2 -Physical quantities Measurement

NUMERICALS – Density & Floatation

Q1. The density of air is 1.28 g litre⁻¹. Express it in: (a) g cm⁻³ (b) kg m⁻³

1 litre = 1000 cm³
(a) Density = 1.28 / 1000 = 0.00128 g cm⁻³

1 g litre⁻¹ = 1 kg m⁻³
(b) = 1.28 kg m⁻³

Q2. The dimensions of a hall are 10 m × 7 m × 5 m. Density of air = 1.11 kg m⁻³. Find mass of air.

Volume = 10 × 7 × 5 = 350 m³
Mass = density × volume = 1.11 × 350 = 388.5 kg

Q3. Density of aluminium = 2.7 g cm⁻³. Convert into kg m⁻³.

1 g cm⁻³ = 1000 kg m⁻³
= 2.7 × 1000 = 2700 kg m⁻³

Q4. Density of alcohol = 600 kg m⁻³. Convert into g cm⁻³.

1 kg m⁻³ = 0.001 g cm⁻³
= 600 × 0.001 = 0.6 g cm⁻³

Q5. Mass of zinc = 438.6 g, Volume = 86 cm³. Find density.

Density = Mass / Volume = 438.6 / 86 = 5.1 g cm⁻³

Q6. A piece of wood has mass 150 g and volume 200 cm³. Find density in: (a) C.G.S. unit (b) S.I. unit

(a) Density = 150 / 200 = 0.75 g cm⁻³
(b) = 0.75 × 1000 = 750 kg m⁻³

Q7. Mass of wood = 6000 kg, density = 0.8 g cm⁻³. Find volume.

Convert density: 0.8 g cm⁻³ = 800 kg m⁻³
Volume = Mass / Density = 6000 / 800 = 7.5 m³

Q8. Mass = 72 g, Initial volume = 24 mL, Final volume = 42 mL. Find density.

Volume = 42 − 24 = 18 cm³
Density = 72 / 18 = 4 g cm⁻³

Q9. Empty bottle = 21 g, with water = 41 g, with liquid = 40.6 g. Find: (a) Volume (b) Relative density

Mass of water = 41 − 21 = 20 g ⇒ Volume = 20 cm³
Mass of liquid = 40.6 − 21 = 19.6 g
Relative density = 19.6 / 20 = 0.98

Q10. Empty bottle = 22 g, with water = 50 g, with brine = 54 g. Find density & relative density.

Mass of water = 28 g ⇒ Volume = 28 cm³
Mass of brine = 32 g
Density = 32 / 28 = 1.14 g cm⁻³
Relative density = 1.14

Q11. Empty bottle = 30 g, with water = 75 g, with liquid = 65 g. Find: (a) Volume (b) Density (c) Relative density

Mass of water = 45 g ⇒ Volume = 45 cm³
Mass of liquid = 35 g
Density = 35 / 45 = 0.78 g cm⁻³
Relative density = 0.78