Mass, Weight and Density - Mathematics Form 1 Notes

• Mass
• Weight
  • Units of Weight
• Density
  • Units of Density
• Past KCSE Questions on the Topic

Mass

• The mass of an object is the quantity of matter in it. Mass is constant quantity, wherever the object is, and matter is anything that occupies space. The three states of matter are solid, liquid and gas.
• The SI unit of mass is the kilogram. Other common units are tone, gram and milligram.
• The following table shows units of mass and their equivalent in kilograms.
  
  

Weight

• The weight of an object on earth is the pull of the earth on it. The weight of any object varies from one place on the earth’s surface to the other. This is because the closure the object is to the centre of the earth, the more the gravitational pull, hence the more its weight. For example, an object weighs more at sea level then on top of a mountain.

Units of Weight

• The SI unit of weight is newton. The pull of the earth, sun and the moon on an object is called the force of gravity due to the earth, sun and moon respectively. The force of gravity due to the earth on an object of mass 1kg is approximately equal to 9.8N. The strength of the earth’s gravitational pull (symbol ‘g’) on an object on the surface of the earth is about 9.8N/Kg.
  
  Weight of an object = mass of an object x gravitation
  Weight N =mass kg x g N/kg

Density

• The density of a substance is the mass of a unit cube of the substance. A body of mass (m)kg and volume (v) m³ has:
  1. Density (d) = mass (m)/ density (d)
  2. Mass (m)= density (d) x volume (v)
  3. Volume (v) = mass (m) / density (d)

Units of Density

• The SI units of density is kg/m³.
• The other common unit is g/cm³
  1 g/cm³ = 1000kg/m³

Example

Find the mass of an ice cube of side 6 cm, if the density of the ice is 0.92 g/ cm³.

Solution

Volume of cube = 6x6x6 = 216 cm³
Mass = density x volume
=21 6 x 0.92
=198.72 g

Example

Find the volume of cork of mass 48 g. given that density of cork is 0.24 g/cm³

Solution

Volume = ^mass/_density
=⁴⁸/_0.24
=200cm³

Example

The density of iron is 7.9 g/cm³. what is this density in kg/m³

Solution

1 g/cm³ = 1 000 kg/m³
7.9 g/cm³ =7.9 x ¹⁰⁰⁰/₁
= 7900kg/m³

Example

A rectangular slab of glass measures 8 cm by 2 cm by 1 4 cm and has a mass of 610g. calculate the density of the glass in kg/m³

Solution

Volume of the slab = 8x 2x1 4
=224 cm³
Mass of the slab = 610 g
Density = ⁶¹⁰/₂₄₄
= 2.5 x 1000 kg = 25 000kg/m³

Past KCSE Questions on the Topic

1. A squared brass plate is 2mm thick and has a mass of 1.05kg. The density of brass is 8.4g/cm³. Calculate the length of the plate in centimeters. (3mks)
2. A sphere has a surface area 18cm². Find its density if the sphere has a mass of 100g. (3mks)
3. Nyahururu Municipal Council is to construct a floor of an open wholesale market whose area is 800m². The floor is to be covered with a slab of uniform thickness of 200mm. In order to make the slab, sand, cement and ballast are to be mixed such that their masses are in the ratio 3:2:3. The mass of dry slab of volume 1m³ is 2000kg. Calculate
   1. 1. The volume of the slab (2mks)
      2. The mass of the dry slab. (2mks)
      3. The mass of cement to be used. (2mks)
   2. If one bag of the cement is 50kg, find the number of bags to be purchased. (1 mk)
      
   3. If a lorry carries 10 tonnes of ballast, calculate the number of lorries of ballast to be  purchased(3mks)
4. A sphere has a surface area of 18.0cm². Find its density if the sphere has a mass of 100 grammes. (3 mks)
5. A piece of metal has a volume of 20 cm³ and a mass of 300g. Calculate the density of the metal in kg/m³.
6. 2.5 litres of water density 1 g/cm³ is added to 8 litres of alcohol density 0.8g/cm³. Calculate the density of the mixture