1. The density of air is 1.28 gram per litre. Express it in:
a) gcm-³
b) kgm-³
Ans.a) density of air is 1.28 gram per litre.
1 litre= 1000ml
= 1000× 1ml
= 1000× 1cm³ (󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈󠄈1cm³ = 1ml)
=1000cm³
Density= 1.28 g / litre
= 1.28 g / 1000 cm³ (1litre = 1000cm³)
= 0.00128 gcm-³
b) density of air is 1.28 gram per litre.
Density= 0.00128 gcm-³
= 0.00128× 1 gcm-³
= 0.00128× 1000 kgm-³ (1 gcm-³= 1000 kgm-³)
= 1.28 kgm-³
2.The dimensions of hall are 10 m×7m×5m. If the density of air is 1.11 kgm-³, find the mass of air in the hall.
Ans. The dimensions of hall are 10m×7m×5m.
l= 10m , b= 7m , h= 5m.
V = l×b×h
V= 10m×7m×5m
= 10 m × 35m²
= 350 m³
Density= mass/volume
Density×volume=mass
Mass=density×volume
= 1.11 kgm-³ × 350 m³
= 1.11×350 kg
=388.5 kg
3. The density of aluminium is 2.7 gram per centimetre cube. Express it in kgm-³.
Ans.
The density of aluminium is 2.7 gram per centimetre cube.
Density= 2.7 gcm-³
= 2.7 × 1 gcm-³
= 2.7 × 1000 kgm-³ (1 gcm-³= 1000 kg -³)
= 2700 kgm-³
4. The density of alcohol is 600 kg per metre cube. Express it in gcm-³.
Ans. The density of alcohol is 600 kg per metre cube.
Density= 600 kgm-³
=600 ×1 kgm-³
= 600 × 1/1000 gcm-³ (1kgm-³= 10-³ gcm-³)
=0.60 gcm-³
5. A piece of zinc of mass fore 38.6 gram has a volume of 86 cm³. Calculate the density of zinc?
Ans.mass=438.6 g
V= 86 cm³
ρ=?
ρ= M/ V
= 438.6 g / 86 cm³
= 5.1 gcm-³
6. A piece of wood of mass 150 gram has a volume of 200 cm³. Find the density of wood in:
a) CGS unit
b) SI unit
Ans.a) M=150g
V = 200 cm³
ρ=?
ρ=M/V
= 150 g / 200 cm³
= 3/4 gcm-³
= 0.75 gcm-³
b) ρ= 0.75 gcm-³
ρ=0.75 × 1 gcm³
= 0.75× 1000 kgm-³ (1g cm-³ = 1000 kgm-³)
= 750 kgm-³
7. Calculate the volume of wood of mass 600 kg if the density of wood is 0.8 gcm-³?
Ans.V= 6000 kg
ρ=0.8 gcm-³
= 0 .8 × 1 gcm-³
= 0.8 × 1000 kgm-³ (1gcm-³=1000kgm-³)
= 800 kgm-³
V=?
ρ= M/V
ρ×V = M
V= M/ ρ
V= 6000kg / 800 kgm-³
= 60/8 kgm-³
= 7.5 kgm-³
8. Calculate the density of a solid from following data:
a) mass of solid= 72 g
b) initial volume of water in measuring cylinder=24ml
c) final volume of water when solid is completely immersed in water= 42ml
Ans.M= 72g
V₁= 24 ml
V₂=42 ml
V=V₂ - V₁
V= 42ml - 24 ml
= 18ml
= 18 × 1 ml
= 18×1cm³ (1ml= 1cm³)
= 18 cm³
ρ= M/V
ρ= 72g / 18 cm³
= 4gcm-³
9. The mass of an empty density bottle is 21.8 gram. When filled completely with water it is 41.8 gram and when filled completely with liquid it is 40.6 gram. Find:
a) the volume of density bottle
b) the relative density of liquid.
Ans.M₁=21.8 g
M₂= 41.8 g
M₃= 40.6 g
Volume of density bottle it's same as the mass of water.
Volume of density bottle= M₂ - M₁
= 41.8g - 21.8 g
= 20.0g
= 20.0×1g (1g = 1 cm³ of water.). = 20.0 cm³
Mass of water= M₂ - M₁
= 41.8 g - 21.8 g
=20.0 g
Mass of liquid=M₃ - M₁
= 40.6 g - 21.8 g
= 18.8 g
Relative density of liquid=( M₃ - M₁)/ (M₂ - M₁)
= 18.8 g / 20.0 g
= 0.94
10. From the following observations,calculate the density and relative density of brine solution. Mass of empty bottle= 22 g
Mass of bottle + water= 50g
Mass of water+brine solution = 54 g
Ans.M₁= 22g
M₂= 50 g
M₃= 54 g
ρ= ?
ρ=M/V
=32 g / 28 cm³
= 1.14 gcm-³
Relative density=mass of brine solution/mass of an equal volume of water.
RD= 32 g / 28 g
= 1.14
11. The mass of an empty density bottle is 30 gram, it is 75 gram when filled completely with water and 65 g when filled completely with liquid. Find:
a) volume of density bottle,
b) density of liquid
c) relative density of liquid.
Ans M₁= 30g
M₂= 75 g
M₃= 65 g
Volume of density bottle= M₂ - M₁
=75 g - 30 g
= 45g
= 45 cm³
Density of liquid= (M₃ - M₁)/ V
= 35g / 45 cm ³
= 0.77 g cm-³
Relative density of liquid= mass of the liquid/mass of an equal volume of water.
Relative density of liquid= 35 g / 45 g
= 0.77
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