Explain with examples the derived units?

Difficulty: Hard

Derived units:

The units used to measure derived quantities are called derived units.

Derived units are defined in terms of base units and are obtained by multiplying or dividing one, or more base units from each other.

Examples:

1. The unit of area (meter)2 and the unit of volume (meter)3 are based on the unit of length, which is meter. Thus, the unit of length is the base unit while the unit of area and volume are derived units.
2. Speed is defined as the distance covered in unit time; therefore, its unit is a meter per second. In the same way, the unit of density, force, pressure, power, etc. can be derived using one or more base units.

Derived quantities and their SI units with symbols

 Quantity Unit Name Symbol Name Symbol Speed V meter per second ms-1 Acceleration A meter per second per second ms-2 Volume V cubic meter m3 Force F newton N or (kg m s2) Pressure P pascal Pa or (N m-2) Density Ρ kilogram per cubic meter Kgm-3 Charge Q coulomb C or (As)

Quick Quiz

1. How can you differentiate between the base and derived quantities?

Ans: Difference between the base and derived quantities:

 Base Quantities Derived Quantities i.    Base quantities are the quantities based on which other quantities are expressed. i. The quantities that are expressed in terms of base quantities are called derived quantities ii. Length, mass, time, electric current, temperature, the intensity of light | and the amount of a substance. ii. Area, volume, speed, force, work, energy, power, electric charge, electric potential, etc.

2. Identify the base quantity is the following:

1. Speed 2. Area 3. Force  4. Distance

The distance can be considered as a base quantity because the distance is equal to the length and its unit is a meter.

1. Speed, area, and force are derived quantities because these quantities are expressed in terms of base quantities.
2. Identify the following as base or derived quantity: density, force, mass, speed, time, length, temperature, and volume.
 Base Quantities Derived Quantities Length, mass, time, temperature. Density, volume, speed, force,

Ans

Mini Exercise

Volume is a derived quantity

1L        = 1000mL

1L       = 1 dm3

= (10cm) 3

= 1000 cm3

1mL = 1 cm3

Express 1 m3 in liters    ......... L

Solution: -1m3 in liters=1000L