Measurements of physical quantities are expressed in terms of units, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners).
The seven fundamental units of SI have been defined as under.
1 kilogram A cylindrical prototype mass made of platinum and iridium alloys of height 39 mm and diameter 39 mm. It is mass of 5.0188 x 1025 atoms of carbon-12.
1 metre 1 metre is the distance that contains 1650763.73 wavelength of orange-red light of Kr-86.
1 second 1 second is the time in which cesium atom vibrates 9192631770 times in an atomic clock.
1 kelvin 1 kelvin is the (1/273.16) part of the thermodynamics temperature of the triple point of water.
1 candela 1 candela is (1/60) luminous intensity of an ideal source by an area of cm’ when source is at melting point of platinum (1760°C).
1 ampere 1 ampere is the electric current which it maintained in two straight parallel conductor of infinite length and of negligible cross-section area placed one metre apart in vacuum will produce between them a force 2 x 10-7 N per metre length.
1 mole 1 mole is the amount of substance of a system which contains a many elementary entities (may be atoms, molecules, ions, electrons or group of particles, as this and atoms in 0.012 kg of carbon isotope 6C12.
Systems of Units
A system of units is the complete set of units, both fundamental and derived, for all kinds of physical quantities. The common system of units which is used in mechanics are given below:
CGS System In this system, the unit of length is centimetre, the unit of mass is gram and the unit of time is second.
FPS System In this system, the unit of length is foot, the unit of mass is pound and the unit of time is second.
MKS System In this system, the unit of length is metre, the unit of mass is kilogram and the unit of time is second.
SI System This system contain seven fundamental units and two supplementary fundamental units.
Relationship between Some Mechanical SI Unit and Commonly Used Units
S.No. Physical Quantity Unit
1 Length (a) 1 micrometre = 10-6 m
(b) 1 angstrom =10-10 m
2 Mass (a) 1 metric ton = 103 kg
(b) 1 pound = 0.4537 kg
(c) 1 amu = 1.66 x10-23 kg
3 Volume 1 litre = 10-32 m3
4. Force (a) 1 dyne = 10-5 N
(b) 1 kgf = 9.81 N
5. Pressure (a) 1 kgfm2 = 9.81Nm-2
(b) 1 mm of Hg = 133 Nm-2
(c) 1 pascal = 1 Nm-2
(d) 1 atmosphere pressure = 76 cm of Hg = 1.01 x 105 pascal
6. Work and energy (a) 1 erg =10-7 J
(b) 1 kgf-m = 9.81 J
(c) 1 kWh = 3.6 x 106 J
(d) 1 eV = 1.6 x 10-19 J
7. Power (d) 1 kgf- ms-1 = 9.81W
1 horse power = 746 W
Some Practical Units
1 fermi =10-15 m
1 X-ray unit = 10-13 m
1 astronomical unit = 1.49 x 1011 m (average distance between sun and earth)
1 light year = 9.46 x 1015 m
1 parsec = 3.08 x 1016 m = 3.26 light year
Some Approximate Masses
Object Kilogram
Our galaxy 2 x 1041
Sun 2 x 1030
Moon 7 x 1022
Asteroid Eros 5 x 1015
Dimensions
Dimensions of any physical quantity are those powers which are raised on fundamental units to express its unit. The expression which shows how and which of the base quantities represent the dimensions of a physical quantity, is called the dimensional formula.
Answers & Comments
Verified answer
Answer:
Measurements of physical quantities are expressed in terms of units, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners).
Answer:
Definitions of Fundamental Units
The seven fundamental units of SI have been defined as under.
1 kilogram A cylindrical prototype mass made of platinum and iridium alloys of height 39 mm and diameter 39 mm. It is mass of 5.0188 x 1025 atoms of carbon-12.
1 metre 1 metre is the distance that contains 1650763.73 wavelength of orange-red light of Kr-86.
1 second 1 second is the time in which cesium atom vibrates 9192631770 times in an atomic clock.
1 kelvin 1 kelvin is the (1/273.16) part of the thermodynamics temperature of the triple point of water.
1 candela 1 candela is (1/60) luminous intensity of an ideal source by an area of cm’ when source is at melting point of platinum (1760°C).
1 ampere 1 ampere is the electric current which it maintained in two straight parallel conductor of infinite length and of negligible cross-section area placed one metre apart in vacuum will produce between them a force 2 x 10-7 N per metre length.
1 mole 1 mole is the amount of substance of a system which contains a many elementary entities (may be atoms, molecules, ions, electrons or group of particles, as this and atoms in 0.012 kg of carbon isotope 6C12.
Systems of Units
A system of units is the complete set of units, both fundamental and derived, for all kinds of physical quantities. The common system of units which is used in mechanics are given below:
CGS System In this system, the unit of length is centimetre, the unit of mass is gram and the unit of time is second.
FPS System In this system, the unit of length is foot, the unit of mass is pound and the unit of time is second.
MKS System In this system, the unit of length is metre, the unit of mass is kilogram and the unit of time is second.
SI System This system contain seven fundamental units and two supplementary fundamental units.
Relationship between Some Mechanical SI Unit and Commonly Used Units
S.No. Physical Quantity Unit
1 Length (a) 1 micrometre = 10-6 m
(b) 1 angstrom =10-10 m
2 Mass (a) 1 metric ton = 103 kg
(b) 1 pound = 0.4537 kg
(c) 1 amu = 1.66 x10-23 kg
3 Volume 1 litre = 10-32 m3
4. Force (a) 1 dyne = 10-5 N
(b) 1 kgf = 9.81 N
5. Pressure (a) 1 kgfm2 = 9.81Nm-2
(b) 1 mm of Hg = 133 Nm-2
(c) 1 pascal = 1 Nm-2
(d) 1 atmosphere pressure = 76 cm of Hg = 1.01 x 105 pascal
6. Work and energy (a) 1 erg =10-7 J
(b) 1 kgf-m = 9.81 J
(c) 1 kWh = 3.6 x 106 J
(d) 1 eV = 1.6 x 10-19 J
7. Power (d) 1 kgf- ms-1 = 9.81W
1 horse power = 746 W
Some Practical Units
1 fermi =10-15 m
1 X-ray unit = 10-13 m
1 astronomical unit = 1.49 x 1011 m (average distance between sun and earth)
1 light year = 9.46 x 1015 m
1 parsec = 3.08 x 1016 m = 3.26 light year
Some Approximate Masses
Object Kilogram
Our galaxy 2 x 1041
Sun 2 x 1030
Moon 7 x 1022
Asteroid Eros 5 x 1015
Dimensions
Dimensions of any physical quantity are those powers which are raised on fundamental units to express its unit. The expression which shows how and which of the base quantities represent the dimensions of a physical quantity, is called the dimensional formula.
Dimensional Formula of Some Physical Quantities
S.No.
Physical
Quantity
Dimensional
Formula
MKS
Unit
1 Area [L2] metre2
2 Volume [L3] metre3
3 Velocity [LT-1] ms-1
4 Acceleration [LT-2] ms-2
5 Force [MLT-2] newton (N)
6 Work or energy [ML2T-2] joule (J)
7 Power [ML2T-3] J s-1 or watt
8 Pressure or stress [ML-1T-2] Nm-2
9 Linear momentum or Impulse [MLT-1] kg ms-1
10 Density [ML-3] kg m-3
11 Strain Dimensionless Unitless
12 Modulus of elasticity [ML-1T-2] Nm-2
13 Surface tension [MT-2] Nm-1
14 Velocity gradient T-1 second-1
15 Coefficient of velocity [ML-1T-1] kg m-1s-1
16 Gravitational constant [M-1L3T-2] Nm2/kg2
17 Moment of inertia [ML2] kg m2
18 Angular velocity [T-1] rad/s
19 Angular acceleration [T-2] rad/S2
20 Angular momentum [ML2T-1] kg m2S-1
21 Specific heat L2T-2θ-1 kcal kg-1K-1
22 Latent heat [L2T-2] kcal/kg
23 Planck’s constant ML2T-1 J-s
24 Universal gas constant [ML2T-2θ-1] J/mol-K