{"id":2816,"date":"2018-05-26T09:12:56","date_gmt":"2018-05-26T01:12:56","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=2816"},"modified":"2023-08-06T14:40:41","modified_gmt":"2023-08-06T14:40:41","slug":"derived-quantities-and-units-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/derived-quantities-and-units-problems-and-solutions.htm","title":{"rendered":"Derived quantities and units \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Derived quantities and units \u2013 problems and solutions<\/span><\/p>\n

1.<\/span><\/p>\n

\"Derived<\/span><\/p>\n

Based on the above table, determine the derived quantities and its international units.<\/span><\/p>\n

Solution<\/span><\/p>\n

Density<\/b><\/span><\/p>\n

The equation of density<\/a> is \u03c1 = m \/ V <\/span><\/p>\n

m = mass<\/a> (its international unit is kilogram, abbreviated kg)<\/span><\/p>\n

V = volume (its international unit is a cubic meter, abbreviated m3<\/sup>)<\/span><\/p>\n

\u03c1 = density (its international unit is kilogram per cubic meter, abbreviated kg\/m3<\/sup>)<\/span><\/p>\n

Force<\/b><\/span><\/p>\n

The equation of force is F = m a<\/span><\/p>\n

m = mass (its international unit is kilogram, abbreviated kg)<\/span><\/p>\n

a = acceleration<\/a> (its international unit is meters per second squared, abbreviated m\/s2<\/sup>)<\/span><\/p>\n

F = force (its international unit is kilogram meters per second squared, abbreviated kg m\/s2<\/sup>)<\/span><\/p>\n

Velocity<\/b><\/span><\/p>\n

The equation of velocity is v = s \/ t<\/span><\/p>\n

s = distance (its international unit is meter, abbreviated m)<\/span><\/p>\n

t = time (its international unit is second, abbreviated s)<\/span><\/p>\n

v = velocity (its international unit is meter per second, abbreviated m\/s)<\/span><\/p>\n

Area<\/b><\/span><\/p>\n

The equation of area is A = l x l<\/span><\/p>\n

l = length (its international unit is meter, abbreviated m)<\/span><\/p>\n

A = area (its international unit is meter squared, abbreviated m2<\/sup>)<\/span><\/p>\n

Temperature<\/b><\/span><\/p>\n

Temperature<\/a> is base quantity. Symbol of temperature is T and its international unit is Kelvin, abbreviated K.<\/span><\/p>\n

The derived quantities and its international units are shown by number (1), (2), and (3).<\/span><\/p>\n

2.<\/span><\/p>\n

\"Derived<\/span><\/p>\n

The derived quantities and its international units are shown by number……<\/span><\/p>\n

Solution<\/span><\/p>\n

(1) Volume: derived quantity<\/span><\/p>\n

(2) Electric current<\/a>: base quantity<\/span><\/p>\n

(3) The intensity of light: base quantity<\/span><\/p>\n

(4) Electric voltage<\/a>: derived quantity<\/span><\/p>\n

(5) Pressure<\/a>: derived quantity<\/span><\/p>\n

The derived quantities and its international units are shown by number (1), (4), and (5)<\/span><\/p>\n

1. Question:<\/strong> What distinguishes a derived quantity from a fundamental or base quantity?<\/span><\/p>\n

Answer:<\/strong> 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.<\/span><\/p>\n

2. Question:<\/strong> What derived quantity is measured in Joules (J)?<\/span><\/p>\n

Answer:<\/strong> Joules measure energy, work, or the amount of heat.<\/span><\/p>\n

3. Question:<\/strong> How is the derived unit for velocity expressed in terms of fundamental units?<\/span><\/p>\n

Answer:<\/strong> Velocity, measured in meters per second (m\/s), is derived from distance (meters) divided by time (seconds).<\/span><\/p>\n

4. Question:<\/strong> Which derived unit represents volume?<\/span><\/p>\n

Answer:<\/strong> The derived unit for volume is the cubic meter (m\u00b3).<\/span><\/p>\n

5. Question:<\/strong> What is the unit of frequency, and how does it relate to time?<\/span><\/p>\n

Answer:<\/strong> The unit for frequency is Hertz (Hz). It represents cycles per second and is the reciprocal of time.<\/span><\/p>\n

6. Question:<\/strong> In what unit do we measure electric capacitance?<\/span><\/p>\n

Answer:<\/strong> Electric capacitance is measured in Farads (F).<\/span><\/p>\n

7. Question:<\/strong> What derived quantity is represented by the unit Pascal (Pa)?<\/span><\/p>\n

Answer:<\/strong> The Pascal (Pa) represents pressure, which is force per unit area.<\/span><\/p>\n

8. Question:<\/strong> How is the unit for acceleration, meters per second squared (m\/s\u00b2), derived?<\/span><\/p>\n

Answer:<\/strong> Acceleration is the rate of change of velocity. Thus, it is derived from dividing velocity (m\/s) by time (s), resulting in m\/s\u00b2.<\/span><\/p>\n

9. Question:<\/strong> What derived quantity does the unit Kelvin per Watt (K\/W) describe?<\/span><\/p>\n

Answer:<\/strong> K\/W describes thermal resistance.<\/span><\/p>\n

10. Question:<\/strong> Which derived unit is used for measuring magnetic flux?<\/span><\/p>\n

Answer:<\/strong> Magnetic flux is measured in Webers (Wb).<\/span><\/p>\n

11. Question:<\/strong> How is the derived unit Ohm (\u03a9) related to electric current and potential difference?<\/span><\/p>\n

Answer:<\/strong> 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.<\/span><\/p>\n

12. Question:<\/strong> In terms of fundamental units, how is the Watt (W) derived?<\/span><\/p>\n

Answer:<\/strong> The Watt represents power, which is energy per unit time. It’s derived as Joules (energy) divided by seconds (time), resulting in kg x m\u00b2\/s\u00b3.<\/span><\/p>\n

13. Question:<\/strong> What is the derived unit for inductance?<\/span><\/p>\n

Answer:<\/strong> The derived unit for inductance is the Henry (H).<\/span><\/p>\n

14. Question:<\/strong> How does the derived unit Newton (N) relate to mass and acceleration?<\/span><\/p>\n

Answer:<\/strong> A Newton represents force. It is derived from mass (kilograms) multiplied by acceleration (m\/s\u00b2).<\/span><\/p>\n

15. Question:<\/strong> What does the derived unit Candela (cd) measure?<\/span><\/p>\n

Answer:<\/strong> Candela measures luminous intensity in a given direction.<\/span><\/p>\n

16. Question:<\/strong> How is the unit for momentum derived?<\/span><\/p>\n

Answer:<\/strong> Momentum is derived by multiplying mass (kg) with velocity (m\/s), resulting in kg x m\/s.<\/span><\/p>\n

17. Question:<\/strong> Which derived unit would you use to measure the amount of substance in moles per volume?<\/span><\/p>\n

Answer:<\/strong> The concentration of a substance in solution is typically measured in moles per cubic meter (mol\/m\u00b3).<\/span><\/p>\n

18. Question:<\/strong> What derived unit is used for measuring electric potential difference?<\/span><\/p>\n

Answer:<\/strong> Electric potential difference is measured in Volts (V).<\/span><\/p>\n

19. Question:<\/strong> What quantity is represented by the derived unit Becquerel (Bq)?<\/span><\/p>\n

Answer:<\/strong> The Becquerel represents radioactivity. Specifically, it’s a measure of the decay rate of radioactive material, indicating one decay per second.<\/span><\/p>\n

20. Question:<\/strong> How is the derived unit for torque, the Newton meter (N\u00b7m), different from the unit for energy, Joule?<\/span><\/p>\n

Answer:<\/strong> While both have the same fundamental units (kg x m\u00b2\/s\u00b2), they represent different physical concepts. N\u00b7m represents torque, which is rotational force, while Joule represents energy or work done.<\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

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