Derived quantities and units – problems and solutions

1.

Based on the above table, determine the derived quantities and its international units.

Solution

**Density**

The equation of density is ρ = m / V

m = mass (its international unit is kilogram, abbreviated kg)

V = volume (its international unit is a cubic meter, abbreviated m^{3})

ρ = density (its international unit is kilogram per cubic meter, abbreviated kg/m^{3})

**Force**

The equation of force is F = m a

m = mass (its international unit is kilogram, abbreviated kg)

a = acceleration (its international unit is meters per second squared, abbreviated m/s^{2})

F = force (its international unit is kilogram meters per second squared, abbreviated kg m/s^{2})

**Velocity**

The equation of velocity is v = s / t

s = distance (its international unit is meter, abbreviated m)

t = time (its international unit is second, abbreviated s)

v = velocity (its international unit is meter per second, abbreviated m/s)

**Area**

The equation of area is A = l x l

l = length (its international unit is meter, abbreviated m)

A = area (its international unit is meter squared, abbreviated m^{2})

**Temperature**

Temperature is base quantity. Symbol of temperature is T and its international unit is Kelvin, abbreviated K.

The derived quantities and its international units are shown by number (1), (2), and (3).

2.

The derived quantities and its international units are shown by number……

Solution

(1) Volume: derived quantity

(2) Electric current: base quantity

(3) The intensity of light: base quantity

(4) Electric voltage: derived quantity

(5) Pressure: derived quantity

The derived quantities and its international units are shown by number (1), (4), and (5)

**1. Question:** What distinguishes a derived quantity from a fundamental or base quantity?

**Answer:** A derived quantity is constructed using combinations of the base quantities through multiplication or division, while a base quantity is fundamental and cannot be derived from other quantities.

**2. Question:** What derived quantity is measured in Joules (J)?

**Answer:** Joules measure energy, work, or the amount of heat.

**3. Question:** How is the derived unit for velocity expressed in terms of fundamental units?

**Answer:** Velocity, measured in meters per second (m/s), is derived from distance (meters) divided by time (seconds).

**4. Question:** Which derived unit represents volume?

**Answer:** The derived unit for volume is the cubic meter (m³).

**5. Question:** What is the unit of frequency, and how does it relate to time?

**Answer:** The unit for frequency is Hertz (Hz). It represents cycles per second and is the reciprocal of time.

**6. Question:** In what unit do we measure electric capacitance?

**Answer:** Electric capacitance is measured in Farads (F).

**7. Question:** What derived quantity is represented by the unit Pascal (Pa)?

**Answer:** The Pascal (Pa) represents pressure, which is force per unit area.

**8. Question:** How is the unit for acceleration, meters per second squared (m/s²), derived?

**Answer:** Acceleration is the rate of change of velocity. Thus, it is derived from dividing velocity (m/s) by time (s), resulting in m/s².

**9. Question:** What derived quantity does the unit Kelvin per Watt (K/W) describe?

**Answer:** K/W describes thermal resistance.

**10. Question:** Which derived unit is used for measuring magnetic flux?

**Answer:** Magnetic flux is measured in Webers (Wb).

**11. Question:** How is the derived unit Ohm (Ω) related to electric current and potential difference?

**Answer:** Ohm is the unit for electrical resistance. It represents the resistance in a circuit where a potential difference of one Volt produces a current of one Ampere.

**12. Question:** In terms of fundamental units, how is the Watt (W) derived?

**Answer:** The Watt represents power, which is energy per unit time. It’s derived as Joules (energy) divided by seconds (time), resulting in kg x m²/s³.

**13. Question:** What is the derived unit for inductance?

**Answer:** The derived unit for inductance is the Henry (H).

**14. Question:** How does the derived unit Newton (N) relate to mass and acceleration?

**Answer:** A Newton represents force. It is derived from mass (kilograms) multiplied by acceleration (m/s²).

**15. Question:** What does the derived unit Candela (cd) measure?

**Answer:** Candela measures luminous intensity in a given direction.

**16. Question:** How is the unit for momentum derived?

**Answer:** Momentum is derived by multiplying mass (kg) with velocity (m/s), resulting in kg x m/s.

**17. Question:** Which derived unit would you use to measure the amount of substance in moles per volume?

**Answer:** The concentration of a substance in solution is typically measured in moles per cubic meter (mol/m³).

**18. Question:** What derived unit is used for measuring electric potential difference?

**Answer:** Electric potential difference is measured in Volts (V).

**19. Question:** What quantity is represented by the derived unit Becquerel (Bq)?

**Answer:** The Becquerel represents radioactivity. Specifically, it’s a measure of the decay rate of radioactive material, indicating one decay per second.

**20. Question:** How is the derived unit for torque, the Newton meter (N·m), different from the unit for energy, Joule?

**Answer:** While both have the same fundamental units (kg x m²/s²), they represent different physical concepts. N·m represents torque, which is rotational force, while Joule represents energy or work done.