Question

units of dimenstions and formulas
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Answer 1

Answer:

Explanation:

Base quantity Unit Symbol

Length Meter M

Mass Kilogram Kg

Time Second Sec

Electric current Ampere A

Answer 2

Derived SI units with Special Names:

Physical quantity SI unit Symbol

Frequency hertz Hz

Energy joule J

Force newton N

Power watt W

Pressure pascal Pa

Electric charge or

quantity of electricity

coulomb C

Electric potential difference and emf volt V

Electric resistance ohm \(\Omega\)

Electric conductance siemen S

Electric capacitance farad F

Magnetic flux weber Wb

Inductance henry H

Magnetic flux density tesla T

Illumination lux Lx

Luminous flux lumen Lm

Dimensional Formulas for Physical Quantities

Physical quantity Unit Dimensional formula

Acceleration or acceleration due to gravity ms–2 LT–2

Angle (arc/radius) rad MoLoTo

Angular displacement rad MoloTo

Angular frequency (angular displacement/time) rads–1 T–1

Angular impulse (torque x time) Nms ML2T–1

Angular momentum (Iω) kgm2s–1 ML2T–1

Angular velocity (angle/time) rads–1 T–1

Area (length x breadth) m2 L2

Boltzmann’s constant JK–1 ML2T–2θ–1

Bulk modulus (\(\Delta P.\frac{V}{\Delta V}\).) Nm–2, Pa M1L–1T–2

Calorific value Jkg–1 L2T–2

Coefficient of linear or areal or volume expansion oC–1 or K–1 θ–1

Coefficient of surface tension (force/length) Nm–1 or Jm–2 MT–2

Coefficient of thermal conductivity Wm–1K–1 MLT–3θ–1

Coefficient of viscosity (F =\(\eta A\frac{dv}{dx}\)) poise ML–1T–1

Compressibility (1/bulk modulus) Pa–1, m2N–2 M–1LT2

Density (mass / volume) kgm–3 ML–3

Displacement, wavelength, focal length m L

Electric capacitance (charge/potential) CV–1, farad M–1L–2T4I2

Electric conductance (1/resistance) Ohm–1 or mho or siemen M–1L–2T3I2

Electric conductivity (1/resistivity) siemen/metre or Sm–1 M–1L–3T3I2

Electric charge or quantity of electric charge (current x time) coulomb IT

Electric current ampere I

Electric dipole moment (charge x distance) Cm LTI

Electric field strength or Intensity of electric field (force/charge) NC–1, Vm–1 MLT–3I–1

Electric resistance (\(\frac{potential\text{ difference}}{current}\)) ohm ML2T–3I–2

Emf (or) electric potential (work/charge) volt ML2T–3I–1

Energy (capacity to do work) joule ML2T–2

Energy density (\(\frac{energy}{volume}\)) Jm–3 ML–1T–2

Entropy (\(\Delta S=\Delta Q/T\)) Jθ–1 ML2T–2θ–1

Force (mass x acceleration) newton (N) MLT–2

Force constant or spring constant (force/extension) Nm–1 MT–2

Frequency (1/period) Hz T–1

Gravitational potential (work/mass) Jkg–1 L2T–2

Heat (energy) J or calorie ML2T–2

Illumination (Illuminance) lux (lumen/metre2) MT–3

Impulse (force x time) Ns or kgms–1 MLT–1

Inductance (L) (energy =\(\frac{1}{2}L{{I}^{2}}\)) or

coefficient of self-induction

henry (H) ML2T–2I–2

Intensity of gravitational field (F/m) Nkg–1 L1T–2

Intensity of magnetization (I) Am–1 L–1I

Joule’s constant or mechanical equivalent of heat Jcal–1 MoLoTo

Latent heat (Q = mL) Jkg–1 MoL2T–2

Linear density (mass per unit length) kgm–1 ML–1

Luminous flux lumen or (Js–1) ML2T–3

Magnetic dipole moment Am2 L2I

Magnetic flux (magnetic induction x area) weber (Wb) ML2T–2I–1

Magnetic induction (F = Bil) NI–1m–1 or T MT–2I–1

Magnetic pole strength (unit: ampere–meter) Am LI

Modulus of elasticity (stress/strain) Nm–2, Pa ML–1T–2

Moment of inertia (mass x radius2) kgm2 ML2

Momentum (mass x velocity) kgms–1 MLT–1

Permeability of free space (\(\mu_o = \frac{4\pi Fd^{2}}{m_1m_2}\)) Hm–1 or NA–2 MLT–2I–2

Permittivity of free space (\({{\varepsilon }_{o}}=\frac{{{Q}_{1}}{{Q}_{2}}}{4\pi F{{d}^{2}}}\).) Fm–1 or C2N–1m–2 M–1L–3T4I2

Planck’s constant (energy/frequency) Js ML2T–1

Poisson’s ratio (lateral strain/longitudinal strain) –– MoLoTo

Power (work/time) Js–1 or watt (W) ML2T–3

Pressure (force/area) Nm–2 or Pa ML–1T–2

Pressure coefficient or volume coefficient oC–1 or θ–1 θ–1

Pressure head m MoLTo

Radioactivity disintegrations per second MoLoT–1

Ratio of specific heats –– MoLoTo

Refractive index –– MoLoTo

Resistivity or specific resistance \(\Omega\)–m ML3T–3I–2

Specific conductance or conductivity (1/specific resistance) siemen/metre or Sm–1 M–1L–3T3I2

Specific entropy (1/entropy) KJ–1 M–1L–2T2θ

Specific gravity (density of the substance/density of water) –– MoLoTo

Specific heat (Q = mst) Jkg–1θ–1 MoL2T–2θ–1

Specific volume (1/density) m3kg–1 M–1L3

Speed (distance/time) ms–1 LT–1

Stefan’s constant\(\left( \frac{heat\ energy}{area\ x\ time\ x\ temperatur{{e}^{4}}} \right)\). Wm–2θ–4 MLoT–3θ–4

Strain (change in dimension/original dimension) –– MoLoTo

Stress (restoring force/area) Nm–2 or Pa ML–1T–2

Surface energy density (energy/area) Jm–2 MT–2

Temperature oC or θ MoLoToθ

Temperature gradient (\(\frac{change\text{ in temperature}}{\text{distance}}\)) oCm–1 or θm–1 MoL–1Toθ

Thermal capacity (mass x specific heat) Jθ–1 ML2T–2θ–1

Time period second T

Torque or moment of force (force x distance) Nm ML2T–2

Universal gas constant (work/temperature) Jmol–1θ–1 ML2T–2θ–1

Universal gravitational constant (F = G. \(\frac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}\)) Nm2kg–2 M–1L3T–2

Velocity (displacement/time) ms–1 LT–1

Velocity gradient (dv/dx) s–1 T–1

Volume (length x breadth x height) m3 L3

Water equivalent kg MLoTo

Work (force x displacement) J ML2T–2