# Dimensions

Dimensions of a Physical Quantity.

The powers to which fundamental quantities must be raised in order to express the given physical quantity are called its dimensions.

To make it more clear, consider the physical quantity force

Force = mass × acceleration mass  x  velocity/ time  = mass × length × (time)–2  -------(i)

Thus, the dimensions of force are 1 in mass, 1 in length and – 2 in time.

Thus equation (i) can be written as [force] = [MLT–2].

Such an expression for a physical quantity in terms of the fundamental quantities is called the dimensional equation. R.H.S. of the equation is termed as dimensional formula.

Thus, dimensional formula for force is, [MLT – 2].

Important Dimensions of Complete Physics.

Mechanics

S. N.

Quantity

Unit

Dimension

1.

Distance or Displacement

m

[M0L1T0]

1.

Velocity or speed (v)

m/s

[M0L1T –1]

1.

Acceleration (a)

m/s2

[M0LT –2]

1.

Momentum (P)

kg-m/s

[M1L1T –1]

1.

Impulse (I)

Newton-sec or kg-m/s

[M1L1T –1]

1.

Force (F)

Newton

[M1L1T –2]

1.

Pressure (P)

Pascal

[M1L–1T 2]

1.

Kinetic energy (EK)

Joule

[M1L2T –2]

1.

Power (P)

Watt or Joule/s

[M1L2T 3]

1.

Density (d)

kg/m3

[M1L– 3T 0]

1.

Angular displacement (q)

[M0L0T 0]

1.

Angular velocity (w)

[M0L0T 1]

1.

Angular acceleration (a)

[M0L0T 2]

1.

Moment of inertia (I)

kg-m2

[M1L2T0]

1.

Torque (t)

Newton-meter

[M1L2T 2]

1.

Angular momentum (L)

Joule-sec

[M1L2T 1]

1.

Force constant or spring constant (k)

Newton/m

[M1L0T –2]

1.

Gravitational constant (G)

N-m2/kg2

[M–1L3T – 2]

1.

Intensity of gravitational field (Eg)

N/kg

[M0L1T – 2]

1.

Gravitational potential (Vg)

Joule/kg

[M0L2T – 2]

1.

Surface tension (T)

N/m or  Joule/m2

[M1L0T 2]

1.

Coefficient of viscosity (h)

kg/m-s

[M1L– 1T – 1]

1.

Stress

N/m2

[M1L– 1T – 2]

1.

Strain

No unit

[M0L0T 0]

1.

Modulus of elasticity (E)

N/m2

[M1L– 1T – 2]

1.

Poisson Ratio (s)

No unit

[M0L0T 0]

Heat

S. N.

Quantity

Unit

Dimension

1.

Temperature (T)

Kelvin

[M0L0T0q 1]

1.

Heat (Q)

Joule

[ML2T– 2]

1.

Specific Heat (c)

Joule/kg-K

[M0L2T– 2q –1]

1.

Thermal capacity

Joule/K

[M1L2T – 2q –1]

1.

Latent heat (L)

Joule/kg

[M0L2T – 2]

1.

Gas constant (R)

Joule/mol-K

[M1L2T2q 1]

1.

Coefficient of thermal conductivity (K)

Joule/m-s-K

[M1L1T– 3q – 1]

1.

Stefan's constant (s)

Watt/m2-K4

[M1L0T– 3q – 4]

1.

Wien's constant (b)

Meter-K

[M0L1Toq1]

1.

Planck's constant (h)

Joule-s

[M1L2T–1]

1.

Coefficient of Linear Expansion (a)

Kelvin–1

[M0L0T0q –1]

1.

Mechanical eq. of Heat (J)

Joule/Calorie

[M0L0T0]

Electrostatics , Electricity and Magnetism

S. N.

Quantity

Unit

Dimension

1.

Electric charge (q)

Coulomb

[M0L0T1A1]

1.

Electric current (I)

Ampere

[M0L0T0A1]

1.

Intensity of electric field (E)

Volt/meter, Newton/coulomb

M1L1T –3A–1

1.

Capacitance (C)

[M–1L– 2T4A2]

1.

Electric potential (V)

Joule/coulomb

M1L2T–3A–1

1.

Permittivity of free space (e0)

Coulomb2/Newton – meter2

[M–1L–3T4A2]

1.

Dielectric constant (K)

Unitless

[M0L0T0]

1.

Resistance (R)

Volt/Ampere or ohm

[M1L2T– 3A– 2]

1.

Resistivity or Specific resistance (r)

Ohm-meter

[M1L3T– 3A– 2]

1.

Coefficient of Self-induction (L)

henery or ohm-second

[M1L2T– 2A– 2]

1.

Magnetic flux (f)

Volt-second or weber

[M1L2T–2A–1]

1.

Magnetic induction (B)

Tesla

[M1L0T– 2A– 1]

1.

Magnetic Intensity (H)

Ampere/meter

[M0L– 1T0A1]

1.

Magnetic Dipole Moment (M)

Ampere-meter2

[M0L2T0A1]

1.

Permeability of Free Space (µ0)

Volt-sec/Ampere-meter or henry/meter

[M1L1T–2A–2]

1.

Surface charge density (s)

Coulomb meter-2

[M0L–2T1A1]

1.

Electric dipole moment (p)

Coulomb meter

[M0L1T1A1]

1.

Conductance (G) (1/R)

Ohm-1

[M–1L–2T3A2]

1.

Conductivity (s) (1/r)

Ohm-1 meter?1

[M–1L–3T3A2]

1.

Current density (J)

Ampere/m2

M0L–2T0A1

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