Here are the 90+ physical quantities that you will encounter in class 11th and 12th physics and have been asked in JEE Main and JEE Advanced exams till date. So, we recommend that you get comfortable with each of these physical quantities. The 33 physical quantities, which student tend to struggle with, have been underlined.
Kinematics [Velocity], [Length]
Force and Motion [Tension] , [Force]
Work Energy Power [Work], [Energy]
Center of Mass and Linear Momentum [Momentum], [Impulse]
Rotation [Torque], [Angular Momentum], [Moment of Inertia], [Moment of a Force]
Gravitation [Gravitational constant, $G$], [$GmM$], [$\cfrac{GM}{R}$], [Gravitational Potential], [Areal Velocity]
Elasiticity [Stress], [Young’s Modulus], [Rigidity Modulus], [Coefficient of Elasticity], [Compressibility]
Fluids [Pressure Gradient], [Coefficient of Viscosity], [Pressure], [Velocity Gradient], [Surface Tension], [Reynolds Number], [Surface Energy]
SHM & Waves [Angular Frequency], [Frequency], [Wave Number], [Wavelength]
Heat and Thermodynamics [Latent Heat], [Wien’s Constant], [Stefan Constant], [Avogardo Number], [Specific Heat Capacity], [Thermal Conductivity], [Heat], [$\cfrac{RT}{M}$], [Entropy]
Electrostatics [Electric Field], [Surface Charge Density], [Electric Potential], [Potential Energy], [Dipole Moment], [$RC$], [Capacitance], [Electric Flux], [Permittivity, $\epsilon_0$], [Electronic Charge, $e$], [Dielectric Constant], [$\cfrac{e^2}{4 \pi \epsilon_0}$]
Current Electricity [Voltage], [EMF], [Potential Difference], [Conductivity], [Resistivity]
Magnetics [Permeability, $\mu_0$], [Magnetic Field], [$\cfrac{F}{qB}$]
Induction and LC Oscillations [Magnetic Induction], [$R$], [$X_L$], [$X_C$], [$\cfrac{R}{X_L X_C}$], [$\cfrac{L}{R}$], [$\sqrt{LC}$], [Displacement Current], [Mutual Inductance], [Power Factor], [Quality Factor], [Relative Permeability, $\mu_r$], [Magnetic Flux], [$L$], [$\cfrac{L}{RC}$], [$LI^2$]
Optics and EM Waves [Refractive Index], [Energy Density], [$\cfrac{1}{\mu_0 \epsilon_0}$], [$\cfrac{B^2}{\mu_0}$], [$\epsilon_0 E^2$], [$\cfrac{E}{B}$], [$\sqrt{\cfrac{\epsilon_0}{\mu_0}}$], [Intensity], [Poynting Vector], [Magnetization], [Coercivity], [Curie], [Light Year]
Modern Physics [Planck’s Constant], [Work Function], [Stopping Potential], [Decay Constant], [Rydberg’s Constant], [$hc$]
Semiconductors [Mobility]
Dimensions of Velocity
Velocity is defined as the rate of change of position per unit time $\equiv \cfrac{dx}{dt}$
$\therefore$ $[\text{Velocity}] = [M^{0} L^{1} T^{-1}]$
Dimensions of Tension
From Newton’s 2nd law, force is equal to mass times acceleration. i.e. $F = ma$
$\therefore$ $[\text{Tension}] = [M^{1} L^{1} T^{-2}]$
Dimensions of Work
Defined as the energy transferred by a force acting on an object as the point of application of force undergoes displacement, $\equiv \overrightarrow{F}.\overrightarrow{dx}$
$\therefore$ $[\text{Work}] = [M^{1} L^{2} T^{-2}]$
Dimensions of Energy
Since all forms of energy will have the same dimensions, recall that kinetic energy of a particle is defined as, $\cfrac{1}{2} mv^2$
$\therefore$ $[\text{Energy}] = [M^{1} L^{2} T^{-2}]$
Dimensions of Momentum
Momentum if defined as product of mass and velocity i.e. $\equiv m \overrightarrow{v}$
$\therefore$ $[\text{Momentum}] = [M^{1} L^{1} T^{-1}]$
Dimensions of Impulse
Impulse is defined as $\equiv F \ dt$, and is equal to, change in momentum i.e. $m \ dv $
$\therefore$ $[\text{Impulse}] = [M^{1} L^{1} T^{-1}]$
Dimensions of Torque
Torque or twisting action of a force is defined as $= \overrightarrow{r} \times \overrightarrow{F}$
$\therefore$ $[\text{Torque}] = [M^{1} L^{2} T^{-2}]$
Dimensions of Angular Momentum
Angular momentum of a particle about a point is given by $= \overrightarrow{r} \times \overrightarrow{p}$, where $\overrightarrow{r}$ is the position vector of the particle and $\overrightarrow{p}$ is the linear momentum ($m v$)
$\therefore$ $[\text{Angular Momentum}] = [M^{1} L^{2} T^{-1}]$
Dimensions of Moment of Inertia
Moment of inertia of a rigid body or a group of particles about an axis is given by $= \sum_i m_i r_i^2$, where $r_i$ is the distance of mass $m_i$ from the axis of rotation.
$\therefore$ $[\text{Moment of Inertia}] = [M^{1} L^{2} T^{0}]$
Dimensions of Moment of a Force
The turning effect of force is known as moment of force same as torque) $\overrightarrow{r} \times \overrightarrow{F}$
$\therefore$ $[\text{Moment of Force}] = [M^{1} L^{2} T^{-2}]$
Dimensions of Gravitational Constant
The gravitational constant, $G$, quantifies the strength of the gravitational interaction between two masses, $F = \cfrac{GmM}{r^2}$
$\therefore$ $[G] = [M^{-1} L^{3} T^{-2}]$
Dimensions of $[GmM]$
Dimensions of $[GmM]$ $= [F][r^2]$ $=[M L^3 T^{-2}]$
Dimensions of $[\cfrac{GM}{R}]$
$\cfrac{GM}{R}$ is simply the gravitational potential, work done by gravitational force on unit test mass, as we move the unit test mass from infinity to the point of interest
$[\cfrac{GM}{R}] = [L^2 T^{-2}]$
Dimensions of Gravitational Potential
Gravitational potential is the work done by gravitational force on a unit test mass, as we move the unit test mass from infinity to the point of interest
$\therefore$ [$\text{Gravitational}$ $\text{Potential}$] $= [L^2 T^{-2}]$
Dimensions of Areal Velocity
Areal velocity is defined as area swept in one sec $\equiv \cfrac{dA}{dt}$
$\therefore$ $[\text{Areal Velocity}] = [M^{0} L^{2} T^{-1}]$
Dimensions of Stress
Stress is simply force per unit area, $\cfrac{F}{A}$
$\therefore$ $[\text{Stress}]$ $= [M^{1} L^{-1} T^{-2}]$
Dimensions of Young's Modulus
Young’s Modulus is defined as the ratio of tensile stress ($\cfrac{F}{A}$) to tensile strain, $\cfrac{dL}{L}$, $Y = \cfrac{\text{Tensile Stress}}{\text{Tensile Strain}}$
$\therefore$ $[\text{Young’s Modulus}]$ $= [M^{1} L^{-1} T^{-2}]$
Dimensions of Rigidity Modulus
Rigidity Modulus is defined as the ratio of shear stress to shear strain $\equiv \cfrac{\text{Shear Stress}}{\text{Shear Strain}}$
$\therefore$ $[\text{Rigidity Modulus}] = [M^{1} L^{-1} T^{-2}]$
Dimensions of Coefficient of Elasticity
Coefficient of Elasticity is defined as the ratio of normal stress to normal strain $\equiv \cfrac{\text{Stress}}{\text{Strain}}$
$\therefore$ $[\text{Coefficient of Elasticity}] = [M^{1} L^{-1} T^{-2}]$
Dimensions of Compressibility
Compressibility is a measure of the relative volume change of a fluid or solid in response to pressure change $\equiv – \cfrac{1}{V} \cfrac{dV}{dp}$
$\therefore$ $[\text{Compressibility}] = [M^{-1} L^{1} T^{2}]$
Dimensions of Pressure Gradient
Pressure Gradient is defined as rate at which pressure changes in a given direction or $\equiv \cfrac{dp}{dx}$
$\therefore$ $[\text{Pressure Gradient}] = [M^{1} L^{-2} T^{-2}]$
Dimensions of Coefficient of Viscosity
Coefficient of Viscosity is defined as the viscous force acting per unit area between two adjacent layers of a liquid such that the velocity gradient is normal to the direction of flow of the liquid. Mathematically it is given as: or $\eta = \cfrac{F}{A \cfrac{dv}{dz}}$
$\therefore$ $[\eta] = [M^{1} L^{-1} T^{-1}]$
Dimensions of Pressue
Pressure is simply force per unit area, i.e. $p = \cfrac{F}{A}$
$\therefore$ $[\text{Pressure}] = [M^{1} L^{-1} T^{-2}]$
Dimensions of Velocity Gradient
Velocity gradient is the change in velocity of the fluid particles as you move a unit distance perpendicular to the flow, $\equiv \cfrac{dV}{dz}$
$\therefore$ $[\text{Velocity Gradient}] = [M^{0} L^{0} T^{-1}]$
Dimensions of Surface Tension
Surface Tension is defined as force per unit length
$\therefore$ $[\text{Surface Tension}] = [M^{1} L^{0} T^{-2}]$
Dimensions of Reynolds Number
Reynolds Number is defined as $ \cfrac{\rho v D}{\eta}$, is a dimensionless quantity
$\therefore$ $[\text{Reynolds Number}] = [M^{0} L^{0} T^{0}]$
Dimensions of Surface Energy
Surface Energy is defined as the work per unit area done by the force that creates the new surface $\equiv T$ (Surface Tension)
$\therefore$ $[\text{Surface Energy}] = [M^{1} L^{0} T^{-2}]$
Dimensions of Angular Frequency
Angular frequency is defined as number of radians per sec $= \cfrac{2 \pi}{T}$ $= 2 \pi f$
$\therefore$ $[\text{Angular Frequency}] = [M^{0} L^{0} T^{-1}]$
Dimensions of Frequency
Frequency is number of oscillations completed in one sec $= \cfrac{1}{T}$ $= \cfrac{\omega}{2 \pi}$
$\therefore$ $[\text{Frequency}] = [M^{0} L^{0} T^{-1}]$
Dimensions of Wave Number
Wave Number is defined as number of waves per unit length $\equiv \cfrac{1}{\lambda}$
$\therefore$ $[\text{Wave Number}] = [M^{0} L^{-1} T^{0}]$
Dimensions of Wavelength
Wavelength is the distance travelled by wave in one time period
$\therefore$ $[\text{Wavelength}] = [M^{0} L^{1} T^{0}]$
Dimensions of Latent Heat
Latent heat is the heat required to convert a unit mass of a solid into a liquid or a unit mass of a liquid into a vapour, without change of temperature $L = \cfrac{Q}{m}$
$\therefore$ [Latent Heat] $= [M^{0} L^{2} T^{-2}]$
Dimensions of Wien's Constant
Wien’s Constant is defined as $b = \lambda_{max} T$
$\therefore$ $[\text{Wien’s Constant}] = [M^{0} L^{1} T^{0} K^{1}]$
Dimensions of Stefan's Constant
Stefan’s Constant, $\sigma = \cfrac{dQ/dt}{\epsilon A T^4}$
$\therefore$ $[\text{Stefans Constant}] = [M^{1} L^{0} T^{-3} K^{-4}]$
Dimensions of Avogardo Number
It is the number of particles in one mole i.e. $N_A = \cfrac{\text{No of particles}}{\text{No. of moles}}$
$\therefore$ [$N_A$] $= [mol^{-1}]$
Dimensions of Specific Heat Capacity
It is the amount of heat required to raise the temperature of a unit mass of a material by 1 degree kelvin or 1 degree $C$ i.e. $c = \cfrac{Q}{m \Delta T}$
$\therefore$ [Specific Heat Capacity] $= [M^{0} L^{2} T^{-2} K^{-1}]$
Dimensions of Thermal Conductivity
It is the rate at which heat is transferred by conduction through a unit cross-sectional area of a material for a unit temperature gradient perpendicular to the area i.e. $K = \cfrac{L}{A \Delta T} \cfrac{dQ}{dt}$
$\therefore$ [K] $= [M^{1} L^{1} T^{-3} K^{-1}]$
Dimensions of Heat
It is the amount of heat required to raise the temperature of a unit mass of a material by 1 degree kelvin or 1 degree $C$ i.e. $c = \cfrac{Q}{m \delta T}$
$\therefore$ [Specific Heat Capacity] $= [M^{0} L^{2} T^{-2} K^{-1}]$
Dimensions of $\cfrac{RT}{M}$
Recall $v_{RMS}^2 = \cfrac{3RT}{M}$. Hence, dimensions of $\cfrac{RT}{M}$ are same as velocity squared
$\therefore$ $[\cfrac{RT}{M}]$ $= [M^{0} L^{2} T^{-2}]$
Dimensions of Entropy
Change in entropy is defined by $= \cfrac{dQ}{T}$
$\therefore$ $[\text{Entropy}] = [M^{1} L^{2} T^{-2} K^{-1}]$
Dimensions of Electric Field
Electric field at a point in space is the force experienced by a unit charge at that point $\overrightarrow{E} = \cfrac{\overrightarrow{F}}{q}$
$\therefore$ [E] $= [M^{1} L^{1} T^{-2} Q^{-1}]$ $= [M^{1} L^{1} T^{-3} A^{-1}]$
Dimensions of Surface Charge Density
Charge per unit area, i.e., $\sigma = \cfrac{Q}{A}$
$\therefore$ [$\sigma$] $= [M^{0} L^{-2} T^{0} Q^{1}]$ $= [M^{0} L^{-2} T^{1} A^{1}]$
Dimensions of Electric Potential
Electric potential difference is defined as the negative of the work done by the electrostatic electric field as we move a unit test charge from some initial point to some final point, $\Delta V = – \cfrac{W}{q}$
$\therefore$ [V] $= [M^{1} L^{2} T^{-2} Q^{-1}]$ $= [M^{1} L^{2} T^{-3} A^{-1}]$
Dimensions of Potential Energy
[Potential Energy] $= [M^{1} L^{2} T^{-2}]$
Dimensions of Dipole Moment
Electric dipole moment, $\overrightarrow{p}$, is defined as $p = qd$
$\therefore$ [Dipole Moment] $= [M^{0} L^{1} T^{0} Q^{1}]$ $= [M^{0} L^{1} T^{1} A^{1}]$
Dimensions of $RC$
Recall the charging RC circuit where charge on the capacitor at time $t$, is given by $q(t) = q_{max} (1 – e^{- \cfrac{t}{RC}})$. And since the power of exponent should be dimensionless, $RC$ should have the same dimensions as time $t$
$\therefore$ [$RC$] $= [M^{0} L^{0} T^{1}]$
Dimensions of Capacitance
Capacitance is defined as the amount of charge, a capacitor can hold, for a unit potential difference across it, i.e. $C = \cfrac{q}{V}$
$\therefore$ [Capacitance] $= [M^{-1} L^{-2} T^{2} Q^{2}]$ $= [M^{-1} L^{-2} T^{4} A^{2}]$
Dimensions of Electric Flux
$\phi_E = \int \overrightarrow{E}.\overrightarrow{dA}$
$\therefore$ [$\phi_E$] $= [M^{1} L^{3} T^{-2} Q^{-1}]$ $= [M^{1} L^{3} T^{-3} A^{-1}]$
Dimensions of Permittivity, $\epsilon_0$
We will use the equation $F = \cfrac{1}{4 \pi \epsilon_0} \cfrac{q_1 q_2}{r^2}$, to determine the dimensions of $\epsilon_0$
$\therefore$ $[\epsilon_0]$ $= [M^{-1} L^{-3} T^{2} Q^{2}]$ $=[M^{-1} L^{-3} T^{4} A^{2}]$
Dimensions of Electronic Charge, $e$
$\therefore$ [$e$] $= [M^{0} L^{0} T^{0} Q^{1}]$ $= [M^{0} L^{0} T^{1} A^{1}]$
Dimensions of Dielectric Constant
Dielectric constant is a dimensionless quantity defined as $\cfrac{\epsilon}{\epsilon_0}$ or $\cfrac{E_0}{E}$
$\therefore$ $[\text{Dielectric Constant}] = [M^{0} L^{0} T^{0}]$
Dimensions of $\cfrac{e^2}{4 \pi \epsilon_0}$
Recall that force between charges, of magnitude $e$, is given by, $F = \cfrac{e^2}{4 \pi \epsilon_0 r^2}$, so dimensions of $ \cfrac{e^2}{4 \pi \epsilon_0}$ are same as that of $[F r^2]$
$\therefore$ [$ \cfrac{e^2}{4 \pi \epsilon_0}$] $= [M^{1} L^{3} T^{-2}]$
Dimensions of EMF
EMF is also known as potential difference and is defined as work done by the battery per unit charge
$\therefore$ $[\text{EMF}] = [M^{1} L^{2} T^{-2} Q^{-1}]$ $= [M^{1} L^{2} T^{-3} A^{-1}]$
Dimensions of Conductivity
Conducticity $ = \cfrac{1}{\text{resistivity}} = \cfrac{J}{E}$, where $J$ is the current density and $E$ is te electric field
$\therefore$ $[\text{Conductivity}] = [M^{-1} L^{-3} T^{1} Q^{2}]$ $= [M^{-1} L^{-3} T^{3} A^{2}]$
Dimensions of Permeability, $\mu_0$
Having found unit of permittivity, $\epsilon_0$, we will use the equation $ \cfrac{1}{\mu_0 \epsilon_0} = c^2$
$\therefore$ $[\text{Permeability, } \mu_0] = [M^{1} L^{1} T^{0} Q^{-2}]$ $= [M^{1} L^{1} T^{-2} A^{-2}]$
Dimensions of Magnetic Induction
Magnetic Induction is given by $B = \cfrac{F}{q v}$
$\therefore$ $[\text{Magnetic Induction}] = [M^{1} L^{0} T^{-1} Q^{-1}]$ $= [M^{1} L^{0} T^{-2} A^{-1}]$
Dimensions of Displacement Current
Displacement current is given by $i_d = \mu_0 \cfrac{d \phi_E}{dt}$, and the dimensions will be same as that of current
$\therefore$ $[\text{Displacement Current}] = [M^{0} L^{0} T^{-1} Q^{1}]$ $= [M^{0} L^{0} T^{0} A^{1}]$
Dimensions of $\bf{\cfrac{R}{\sqrt{X_L X_C}}}$
Note that $X_L$ and $X_C$ have the same units/dimensions as $R$, so $\cfrac{R}{\sqrt{X_L X_C}}$ will be dimensionless
i.e $\therefore$ $[\cfrac{R}{\sqrt{X_L X_C}}] = [M^{0} L^{0} T^{0}]$
Dimensions of Mutual Inductance
Mutual Inductance is defined as magnetic flux through coil ‘1’ per unit current in coil ‘2’ , i.e. $\cfrac{\phi_1}{i_2}$
$\therefore$ $[\text{Mutual Inductance}] = [M^{1} L^{2} T^{0} Q^{-2}]$ $= [M^{1} L^{2} T^{-2} A^{-2}]$
Dimensions of Power Factor
Power factor is defined as the ratio of real power absorbed by the load to the apparent power flowing in the circuit, note or $P = I_{rms} V_{rms} \cos \phi$, where $\cos \phi$ is the power factor and is thus dimensionless
$\therefore$ $[\text{Power Factor}] = [M^{0} L^{0} T^{0}]$
Dimensions of Quality Factor
$Q = \cfrac{\omega_r L}{R}$ and is thus dimensionless, note the reactance of an inductor $X_L = \omega L$ has the same units/dimensions as that of resistance $R$
$\therefore$ $[\text{Quality Factor}] = [M^{0} L^{0} T^{0}]$
Dimensions of $\bf{\cfrac{L}{RC}}$
Recall from the charging or discharging RC circuits that $RC$ which represented time constant there, had the units of time i.e. $[\tau] = [T]$, so
$\therefore$ $[\cfrac{L}{RC}] = [M^{1} L^{2} T^{-1} Q^{-2}]$ $= [M^{1} L^{2} T^{-3} A^{-2}]$
Dimensions of Intensity
Intensity is defined as the amount of energy passing through a unit area in unit time $\equiv \cfrac{[Q]}{[A][T]}$
$\therefore$ $[\text{Intensity}] = [M^{1} L^{0} T^{-3}]$
Dimensions of Poynting Vector
$\overrightarrow{S} = \cfrac{1}{\mu_0} \overrightarrow{E} \times \overrightarrow{B}$, and has the same units as Intensity
$\therefore$ $[\text{Poynting Vector}] = [M^{1} L^{0} T^{-3}]$
Dimensions of Magnetization
Magnetization is defined as magnetic moment per unit volume. And recall that magnetic moment of a coil carrying current ‘$i$’ is $=iA$, where $A$ is the area of the loop.
$\therefore$ $[\text{Magnetization}] = [M^{0} L^{-1} T^{1} Q^{1}]$ $= [M^{0} L^{-1} T^{2} A^{1}]$
Dimensions of Coercivity
Coercivity is defined as the magnetizing field, $H$, needed to demagnetize the magnetic material completely and recall that $\overrightarrow{B} = \mu_0 (\overrightarrow{M} + \overrightarrow{H})$, meaning that magnetization $M$ and magnetizing field $H$ have the same dimensions
$\therefore$ $[\text{Coercivity}] = [M^{0} L^{-1} T^{1} Q^{1}]$ $= [M^{0} L^{-1} T^{2} A^{1}]$
Dimensions of Curie
Recall that $M = C \cfrac{B}{T}$, where $C$ is the curie’s constant
$\therefore$ $[\text{Curie}] = [M^{-1} L^{-1} T^{2} Q^{2} K^{1}]$ $= [M^{-1} L^{-1} T^{4} A^{2} K^{1}]$
Dimensions of Rydberg's Constant
defined as $\cfrac{13.6 eV}{hc}$ $m^{-1}$
$\therefore$ $[\text{Rydberg’s Constant}] = [M^{0} L^{-1} T^{0}]$
Dimensions of Mobility
Mobility is defined as drift velocity per unit electric field i.e. $= \cfrac{v_d}{E}$
$\therefore$ $[\text{Mobility}] = [M^{-1} L^{0} T^{1} Q^{1}]$ $= [M^{-1} L^{0} T^{2} A^{1}]$
