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Unit & Dimension formulas

Master Unit & Dimension through 30 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Unit & Dimension, every formula

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Dimensions of force
$[F] = M L T^{- 2}$
Q1MCQForce
The dimensional formula of force is:
- A
  $MLT^{-2}$
- B
  $ML^{2}T^{-2}$
- C
  $MLT^{-1}$
- D
  $ML^{-1}T^{-2}$
Dimensions of work/energy
$[W] = M L^{2} T^{- 2}$
Q1MCQEnergy
The dimensional formula of energy is:
- A
  $ML^{2}T^{-2}$
- B
  $MLT^{-2}$
- C
  $ML^{2}T^{-3}$
- D
  $ML^{2}T^{-1}$
Dimensions of power
$[P] = M L^{2} T^{- 3}$
Q1MCQPower
The dimensional formula of power is:
- A
  $ML^{2}T^{-3}$
- B
  $ML^{2}T^{-2}$
- C
  $MLT^{-3}$
- D
  $ML^{2}T^{-1}$
Dimensions of pressure
$[P] = M L^{- 1} T^{- 2}$
Q1MCQPressure
The dimensional formula of pressure is:
- A
  $ML^{-1}T^{-2}$
- B
  $MLT^{-2}$
- C
  $ML^{2}T^{-2}$
- D
  $ML^{-3}$
Dimensions of momentum
$[p] = M L T^{- 1}$
Q1MCQMomentum
The dimensional formula of momentum is:
- A
  $MLT^{-1}$
- B
  $MLT^{-2}$
- C
  $ML^{2}T^{-1}$
- D
  $MLT$
Dimensions of velocity
$[v] = L T^{- 1}$
Q1MCQVelocity
The dimensional formula of velocity is:
- A
  $LT^{-1}$
- B
  $LT^{-2}$
- C
  $L^{2}T^{-1}$
- D
  $LT$
Dimensions of acceleration
$[a] = L T^{- 2}$
Q1MCQAcceleration
The dimensional formula of acceleration is:
- A
  $LT^{-2}$
- B
  $LT^{-1}$
- C
  $L^{2}T^{-2}$
- D
  $MLT^{-2}$
Dimensions of density
$[ρ] = M L^{- 3}$
Q1MCQDensity
The dimensional formula of density is:
- A
  $ML^{-3}$
- B
  $ML^{3}$
- C
  $ML^{-1}$
- D
  $M^{-1}L^{3}$
Dimensions of frequency
$[f] = T^{- 1}$
Q1MCQFrequency
The dimensional formula of frequency is:
- A
  $T^{-1}$
- B
  $T$
- C
  $LT^{-1}$
- D
  $T^{-2}$
Dimensions of charge
$[q] = A T$
Q1MCQCharge
The dimensional formula of electric charge is:
- A
  $AT$
- B
  $\dfrac{A}{T}$
- C
  $A$
- D
  $AT^{-1}$
Dimensions of G
$[G] = M^{- 1} L^{3} T^{- 2}$
Q1MCQG
The dimensional formula of the gravitational constant $G$ is:
- A
  $M^{-1}L^{3}T^{-2}$
- B
  $MLT^{-2}$
- C
  $M^{-1}L^{2}T^{-2}$
- D
  $ML^{3}T^{-2}$
Dimensions of Planck's constant
$[h] = M L^{2} T^{- 1}$
Q1MCQPlanck's constant
The dimensional formula of Planck's constant is:
- A
  $ML^{2}T^{-1}$
- B
  $ML^{2}T^{-2}$
- C
  $MLT^{-1}$
- D
  $ML^{2}T^{-3}$
Dimensions of ε₀
$[ε_{0}] = M^{- 1} L^{- 3} T^{4} A^{2}$
Q1MCQε₀
The dimensional formula of $\varepsilon_0$ is:
- A
  $M^{-1}L^{-3}T^{4}A^{2}$
- B
  $MLT^{-2}A^{-2}$
- C
  $M^{-1}L^{-3}T^{2}A^{2}$
- D
  $MLT^{4}A^{2}$
Dimensions of μ₀
$[μ_{0}] = M L T^{- 2} A^{- 2}$
Q1MCQμ₀
The dimensional formula of $\mu_0$ is:
- A
  $MLT^{-2}A^{-2}$
- B
  $M^{-1}L^{-3}T^{4}A^{2}$
- C
  $MLT^{-2}A^{2}$
- D
  $ML^{2}T^{-2}$
Dimensions of viscosity
$[η] = M L^{- 1} T^{- 1}$
Q1MCQViscosity
The dimensional formula of coefficient of viscosity is:
- A
  $ML^{-1}T^{-1}$
- B
  $MLT^{-1}$
- C
  $ML^{-1}T^{-2}$
- D
  $MT^{-2}$
Dimensions of surface tension
$[σ] = M T^{- 2}$
Q1MCQSurface tension
The dimensional formula of surface tension is:
- A
  $MT^{-2}$
- B
  $MLT^{-2}$
- C
  $ML^{-1}T^{-2}$
- D
  $MT^{-1}$
Dimensions of angular momentum
$[L] = M L^{2} T^{- 1}$
Q1MCQAngular momentum
The dimensional formula of angular momentum is:
- A
  $ML^{2}T^{-1}$
- B
  $MLT^{-1}$
- C
  $ML^{2}T^{-2}$
- D
  $ML^{2}T^{-3}$
Dimensions of impulse
$[J] = M L T^{- 1}$
Q1MCQImpulse
The dimensional formula of impulse is:
- A
  $MLT^{-1}$
- B
  $MLT^{-2}$
- C
  $ML^{2}T^{-1}$
- D
  $ML^{2}T^{-2}$
Dimensions of electric field
$[E] = M L T^{- 3} A^{- 1}$
Q1MCQElectric field
The dimensional formula of electric field is:
- A
  $MLT^{-3}A^{-1}$
- B
  $ML^{2}T^{-3}A^{-1}$
- C
  $MLT^{-2}A^{-1}$
- D
  $MLT^{-3}A$
Dimensions of potential
$[V] = M L^{2} T^{- 3} A^{- 1}$
Q1MCQPotential
The dimensional formula of electric potential is:
- A
  $ML^{2}T^{-3}A^{-1}$
- B
  $MLT^{-3}A^{-1}$
- C
  $ML^{2}T^{-2}A^{-1}$
- D
  $ML^{2}T^{-3}A$
Dimensions of resistance
$[R] = M L^{2} T^{- 3} A^{- 2}$
Q1MCQResistance
The dimensional formula of resistance is:
- A
  $ML^{2}T^{-3}A^{-2}$
- B
  $ML^{2}T^{-3}A^{-1}$
- C
  $MLT^{-3}A^{-2}$
- D
  $ML^{2}T^{-2}A^{-2}$
Dimensions of capacitance
$[C] = M^{- 1} L^{- 2} T^{4} A^{2}$
Q1MCQCapacitance
The dimensional formula of capacitance is:
- A
  $M^{-1}L^{-2}T^{4}A^{2}$
- B
  $ML^{2}T^{-4}A^{-2}$
- C
  $M^{-1}L^{-2}T^{2}A^{2}$
- D
  $ML^{-2}T^{4}A^{2}$
Dimensions of magnetic field
$[B] = M T^{- 2} A^{- 1}$
Q1MCQMagnetic field
The dimensional formula of magnetic field is:
- A
  $MT^{-2}A^{-1}$
- B
  $MLT^{-2}A^{-1}$
- C
  $MT^{-2}A$
- D
  $ML^{2}T^{-2}A^{-1}$
Principle of homogeneity
$all terms in an equation have the same dimensions$
Q1MCQHomogeneity
The principle of homogeneity requires that:
- A
  all terms in an equation have the same dimensions
- B
  the equation is linear
- C
  all constants are dimensionless
- D
  the units are SI
Unit conversion
$n_{1} u_{1} = n_{2} u_{2}$
Q1MCQUnit conversion
When converting a physical quantity between unit systems:
- A
  $n_1 u_1=n_2 u_2$
- B
  $n_1 u_1=n_2/u_2$
- C
  $n_1=n_2$
- D
  $u_1=u_2$
Angstrom
$1 \overset{˚}{A} = 1 0^{- 10} m$
Q1MCQAngstrom
One angstrom equals:
- A
  $10^{-10}$ m
- B
  $10^{-15}$ m
- C
  $10^{-9}$ m
- D
  $10^{-6}$ m
Light year
$1 ly = 9.46 \times 1 0^{15} m$
Q1MCQLight year
One light year is approximately:
- A
  $9.46\times10^{15}$ m
- B
  $3.08\times10^{16}$ m
- C
  $1.49\times10^{11}$ m
- D
  $10^{10}$ m
Parsec
$1 pc = 3.08 \times 1 0^{16} m$
Q1MCQParsec
One parsec is approximately:
- A
  $3.08\times10^{16}$ m
- B
  $9.46\times10^{15}$ m
- C
  $1.49\times10^{11}$ m
- D
  $10^{10}$ m
Astronomical unit
$1 AU = 1.49 \times 1 0^{11} m$
Q1MCQAstronomical unit
One astronomical unit is approximately:
- A
  $1.49\times10^{11}$ m
- B
  $9.46\times10^{15}$ m
- C
  $3.08\times10^{16}$ m
- D
  $10^{8}$ m
Dimensionless quantities
$angle, strain, refractive index, relative density$
Q1MCQDimensionless
Which quantity is dimensionless?
- A
  strain
- B
  force
- C
  velocity
- D
  density

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Unit & Dimension formulas

Unit & Dimension, every formula

Dimensions of force

Dimensions of work/energy

Dimensions of power

Dimensions of pressure

Dimensions of momentum

Dimensions of velocity

Dimensions of acceleration

Dimensions of density

Dimensions of frequency

Dimensions of charge

Dimensions of G

Dimensions of Planck's constant

Dimensions of ε₀

Dimensions of μ₀

Dimensions of viscosity

Dimensions of surface tension

Dimensions of angular momentum

Dimensions of impulse

Dimensions of electric field

Dimensions of potential

Dimensions of resistance

Dimensions of capacitance

Dimensions of magnetic field

Principle of homogeneity

Unit conversion

Angstrom

Light year

Parsec

Astronomical unit

Dimensionless quantities

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