Derived quantities and units – problems and solutions

Derived quantities and units – problems and solutions

1.

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 m3)

ρ = density (its international unit is kilogram per cubic meter, abbreviated kg/m3)

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/s2)

F = force (its international unit is kilogram meters per second squared, abbreviated kg m/s2)

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 m2)

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.

Derived quantities and units – problems and solutions 2

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

Solution

(1) Volume: derived quantity

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(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)?

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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?

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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.

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