i)

Fundamental units of measurement

1. Metre
2. Second
3. Kilogram
4. Degree celcius/kelvin

ii)

Physical quantity that the units named in (i) measures

1. Metre → length
2. Second → time
3. Kilogram → mass
4. Degree celcius/kelvin → temperature

(i)

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

Volume = Final volume - Initial volume

Volume = 90 cm³ - 60 cm³
Volume = 30.0 cm³

Density = $\frac{\mathrm{36.0\; g}}{30.0{cm}^3}$

Density = 1.2 gcm^-3

(ii)

The stone will float in the liquid because the density of the stone is less than that of the liquid.

(i)

(ii)

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

Volume = $\frac{\mathrm{Mass}}{\mathrm{Density}}$

Density = 0.9 g/cm³

Mass = 300 g

Volume = $\frac{300}{0.9}$ cm³

0.9 = $\frac{9}{10}$

Volume = 300 ÷ $\frac{9}{10}$ cm³

Reciprocate the fraction at the right of ÷ and change the ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

Volume = 300 x $\frac{10}{9}$ cm³

Volume = $\frac{\mathrm{300\; x\; 10}}{9}$ cm³

Volume = $\frac{3000}{9}$ cm³

Volume = 333.33 cm³

i)

Density is defined as mass per unit volume of a substance

OR

Density = $\frac{\mathrm{Mass\; of\; substance}}{\mathrm{Volume\; of\; substance}}$

ii)

How to make a body which sinks in water float

1. Make the body hollow/shape body into a bowl
2. Decrease the density of the body to lower than the density of water by increasing the volume of the body

i)

Density of a substance is the mass per unit volume of the substance.

OR

Density = $\frac{\mathrm{Mass\; (M)}}{\mathrm{Volume\; (V)}}$

ii)

Determination of the density of a stone

1. Measure/weigh the mass of stone by means of a beam/chemical balance as M g
2. Fill a large measuring cylinder with water to a suitable level and record the volume as V₁ cm³
3. Tie the stone with thread and gently lower it into the water in the measuring cylinder and record the new volume as V₂ cm³

The density of the stone is then calculated as follows:

Volume of stone = V₂ cm³ - V₁ cm³

Mass of stone = M g

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

Density of the stone = $\frac{\mathrm{M\; g}}{({\mathrm{V}}_2-{\mathrm{V}}_1){\mathrm{cm}}^3}$

(i)

Density of a substance is the mass per unit volume of the substance.

OR

Density = $\frac{\mathrm{Mass\; (M)}}{\mathrm{Volume\; (V)}}$

(ii)

Determination of the density of an irregular piece of stone

1. Measure/weigh the mass of stone by means of a beam/chemical balance as M g
2. Fill a large measuring cylinder with water to a suitable level and record the volume as V₁ cm³
3. Tie the stone with thread and gently lower it into the water in the measuring cylinder and record the new volume as V₂ cm³

The density of the stone is then calculated as follows:

Volume of stone = V₂ cm³ - V₁ cm³

Mass of stone = M g

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

Density of the stone = $\frac{\mathrm{M\; g}}{({\mathrm{V}}_2-{\mathrm{V}}_1){\mathrm{cm}}^3}$

(iii)

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

Volume = 1200.0 m³

Density = 1.95 kgm^-3

Mass = Density x Volume

Mass = 1200.0 m³ x 1.95 kgm^-3

Mass = 2340 kg

(i)

Power → Watts (W)

(ii)

Energy → Joules (J)

(iii)

Electric current → Amperes (A)

(iv)

Temperature → Kelvin (K)/Degree celsius (°C)

(i)

Change in volume = (75 - 50) cm³ = 25 cm³

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

Method I

Calculating density in kg dm^-3

Note: when using the mass in kilogram (4 kg) the volume must be in dm³.

25 cm³ = $\frac{25}{1000}$ = 0.025 dm³

Density = $\frac{4}{0.025}$ = 160 kg dm^-3 or 160 kg/dm³

Method II

Calculating density in g cm^-3

Note: when expressing the density in g cm^-3, the kilogram must be changed to gram.

4 kg = 4 x 1000 g = 4000 g

Density = $\frac{4000}{25}$ = 160 g cm^-3 or 160 g/cm³

Note: Mark is deducted for answer without correct unit

(ii)

Precautions that must be taken to obtain reliable results

1. The object should be dropped gently to avoid splashing the water
2. The volume should be read at the correct meniscus

(i)

A physical quantity is any physical property of a material or substance that can be quantified, that is, can be measured using numbers

(ii)

1. Mass
2. Force
3. Density
4. Length
5. Temperature
6. Volume
7. Electric current
8. Velocity
9. Time

(i)

Density is the mass per unit volume of a substance

OR

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

(ii)

How yto determine the density of a sample of soil

Method I

1. The mass of an empty wooden rectangular box is measured by means of a beam balance and the result is recorded as M₁ g
2. The rectangular box is filled to the brim with the sample of soil
3. The mass of the box containing the sample of soil is measured by means of a beam balance and the result is recorded as M₂ g
4. The length, breadth and height of the box is measured

Calculations

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

Mass of soil sample = (M₂ - M₁) g

The volume of the box equals to the volume of the soil sample since the box is filled to the brim with the soil

Volume of soil sample = Length x Breadth x Height of box = V cm³

Density of soil = $\frac{{\mathrm{M}}_2-{\mathrm{M}}_1}{\mathrm{V}}$ g/cm³

Method II

1. The mass of the soil sample is measured by means of a beam balance and the result recorded as M g

2. Water is poured into a measuring cylinder to a suitable level/about half full and the initial level of water recorded as V₁ cm³

3. The soil sample is gently poured into the measuring cylinder containing the water
4. The level of the water goes up and this new level of water is recorded as V₂ cm³

Calculations

Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$

Mass of soil sample = M g

Volume of soil sample = (V₂ - V₁)cm³

Density of soil = $\frac{\mathrm{M}}{{\mathrm{V}}_2-{\mathrm{V}}_1}$ g/cm³

i)

Length of a rope → Metre rule/tape measure/ruler/surveyor's tape

ii)

Mass of a stone → Beam balance/chemical balance/top pan balance/electronic balance

iii)

Temperature of a liquid → Thermometer

iv)

Volume of a liquid → Volumetric flask/pipette/graduated cylinder/measuring cylinder/burette/graduated beaker

i)

Derrived quantities are quantities which are combination/multiples/ratios of base/fundamental quantities

ii)

S.I. units of area and volume

i)

Mass is the amount of substance (matter) in a body or particle

Is a measure of how much matter is in an object

ii)

Density = Mass / Volume

Mass = Density x Volume

Density = 2.0 g cm^-3, Length = 3 cm

Length of a cuboid (Equal size) = Length x Length x Length

Volume of the box = 3 cm x 3 cm x 3 cm = 27.0 cm³

Mass = 2.0 g cm^-3 x 27.0 cm³ = 54.0 g