Mechanics
Physical Quantity
This is the quantity by means of which we can describe the laws of physics. e.g. force, torque, work, velocity etc. The physical quantities are of two kinds
Fundamental physical quantities
Derived physical quantities
This is the quantity by means of which we can describe the laws of physics. e.g. force, torque, work, velocity etc. The physical quantities are of two kinds
Fundamental physical quantities
Derived physical quantities
Fundamental Physical Quantities
FPQ Unit (SI) Symbol Dimension
length meter m L
mass kilogram kg M
Time second s T
electric current Ampere A A or I
temperature Kelvin K K or θ
luminous intensity candela c or cd c or cd
amount of substance mole mol mol or N
Derived Physical Quantity
Physical quantities that are derived from fundamental physical quantities are called derived physical quantities. e.g. velocity, pressure etc.
Principle of measurement
nu = constant
i.e. n1u1 = n2u2
where n is numeric value and u is standard unit.
FPQ Unit (SI) Symbol Dimension
length meter m L
mass kilogram kg M
Time second s T
electric current Ampere A A or I
temperature Kelvin K K or θ
luminous intensity candela c or cd c or cd
amount of substance mole mol mol or N
Derived Physical Quantity
Physical quantities that are derived from fundamental physical quantities are called derived physical quantities. e.g. velocity, pressure etc.
Principle of measurement
nu = constant
i.e. n1u1 = n2u2
where n is numeric value and u is standard unit.
Unit
It is a standard amount for a physical quantity used for measurement. There are 3 kinds of units.
Fundamental Unit: units of fundamental physical quantity.
Supplementary Unit: units of plane angle and solid angle.
Derived Units: units of derived physical quantities.
It is a standard amount for a physical quantity used for measurement. There are 3 kinds of units.
Fundamental Unit: units of fundamental physical quantity.
Supplementary Unit: units of plane angle and solid angle.
Derived Units: units of derived physical quantities.
Dimension
When physical quantities are expressed as a function of fundamental quantities in the form of product, then power to those fundamental quantities is called dimension e.g.
W = F d = ma d = m (d/t) d = [ML2T-2]
Uses of Dimension
Testing correctness of a relation.
Identifying unknown quantity in a relation.
Derivation of relation for a physical quantity.
Conversion from one system to another system of unit.
When physical quantities are expressed as a function of fundamental quantities in the form of product, then power to those fundamental quantities is called dimension e.g.
W = F d = ma d = m (d/t) d = [ML2T-2]
Uses of Dimension
Testing correctness of a relation.
Identifying unknown quantity in a relation.
Derivation of relation for a physical quantity.
Conversion from one system to another system of unit.
Q. Which of the following quantity is dimensional quantity?
(a) Angle (b) strain (c) relative density (d) relative velocity
Ans: (d)
relative velocity is difference of two velocities.
Q. Which of the following is a dimensional constant?
(a) Dielectric constant (b) refractive index (c) stafene constant (d) relative density
Ans: (c)
Dielectric constant = ϵ / ϵo
refractive index = c / v
stafene constant = E / T4
relative density = Dmedium / Dwater
Q. A dimensionless quantity is
(a) always unit less (b) never unit less (c) may have unit (d) never exits.(a) Angle (b) strain (c) relative density (d) relative velocity
Ans: (d)
relative velocity is difference of two velocities.
Q. Which of the following is a dimensional constant?
(a) Dielectric constant (b) refractive index (c) stafene constant (d) relative density
Ans: (c)
Dielectric constant = ϵ / ϵo
refractive index = c / v
stafene constant = E / T4
relative density = Dmedium / Dwater
Q. A dimensionless quantity is
Ans: (c)
Note:- Dimension less physical quantities may have units but unit less quantities are always dimension less e.g. plane angle (unit radian), solid angle (unit stradian), mechanical equivalent of heat (cal/J), Loudness of sound (unit Bell) are dimension less but they have unit.
Dimensionless Quantities
Relative density ( ρ = ρm / ρw)
Plane angel ( θ = s / r)
Solid angle (ω = A / r2 )
Strain ( = Δl / l)
Poission's ratio ( Pr = Δd/d ₓ l/Δl )
Loudness ( L = log(I / Io))
Mechanical equivalent of Heat ( J = W / H)
Emissivity (E = e / eb)
Relative permitivity or dielectric constant (K = ϵr = ϵ / ϵo )
Relative permeability (μr = μ / μo )
Refractive index (μ = c / v)
Magnification (m = v / u)
Dispersive power (ω = (δv - δr) / δ )
Quantities Having Identical Dimensions
Acceleration (a or g) and Gravitational field strength (E=mg/m) have dimension [M0L1T-2]
Force and Energy gradient (F*l/l = F) have dimension [M1L1T-2]
Surface tension (=F/l) and Spring constant (k=F/x) have dimenion [M1L0T-2]
Angular velocity (ω=2πf), frequency (f), velocity gradient (v/l = l/tl = f), radioactive decay constant have dimension [M0L0T-1]
Pressure (=F/A), stress (=F/A), elastic modulii (γ,Ƞ,k=stress/strain), energy density (Fl/Al) have dimension [M1L-1T-2]
Work (=F*l), energy, torque (=r ₓ F) have dimension [M1L2T-2]
Force and Energy gradient (F*l/l = F) have dimension [M1L1T-2]
Surface tension (=F/l) and Spring constant (k=F/x) have dimenion [M1L0T-2]
Angular velocity (ω=2πf), frequency (f), velocity gradient (v/l = l/tl = f), radioactive decay constant have dimension [M0L0T-1]
Pressure (=F/A), stress (=F/A), elastic modulii (γ,Ƞ,k=stress/strain), energy density (Fl/Al) have dimension [M1L-1T-2]
Work (=F*l), energy, torque (=r ₓ F) have dimension [M1L2T-2]
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