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Hello learner, hope you are doing great. Today we will be studying about the Dimensions of Physical quantity.

Let&#39;s firstly know what is dimensions of a physical quantity. Dimensions of a physical quantity are the powers or exponents to which the fundamental quantities must be raised to represent that quantity completely. Suppose there is a new quantity (a quantity for which the dimensional formula is unknown). Now if we want to derive a dimensional formula for this particular quantity, we would have used the fundamental quantities that we already know and we have to raise the fundamental quantities to a certain power (or exponents) in order to derive dimensions of this new quantity. For example, Density = mass/volume, Dimensions of density = [ML-3 ] = [M1L -3T 0 ]

All the derived physical quantities of the world can be expressed in terms of some combinations of the seven fundamental or base quantities. We call these fundamental quantities as the seven dimensions of the world, they are

<ol>
	<li>Dimension of length = [L]</li>
	<li>Dimension of mass = [M]</li>
	<li>Dimension of time = [T]</li>
	<li>Dimension of electric current = [A]</li>
	<li>Dimension of thermodynamic temperature = [K]</li>
	<li>Dimension of luminous intensity = [cd]</li>
	<li>Dimension of amount of substance = [mol]</li>
</ol>

Dimensional Formula:

<table cellspacing="0" class="Table" style="border-collapse:collapse; border:none; margin-left:14px; width:300px">
	<tbody>
		<tr>
			<td>
			Sr.

			No.
			</td>
			<td>
			Physical Quantity
			</td>
			<td>
			Relation with other quantities
			</td>
			<td>
			Dimensional formula
			</td>
			<td>
			SI Unit 
			</td>
		</tr>
		<tr>
			<td>
			1
			</td>
			<td>
			area
			</td>
			<td>
			Length × breadth
			</td>
			<td>
			[M0L2T0 ]
			</td>
			<td>
			m2
			</td>
		</tr>
		<tr>
			<td>
			2
			</td>
			<td>
			volume
			</td>
			<td>
			Length × breadth × height
			</td>
			<td>
			[M0L3T0 ]
			</td>
			<td>
			m3
			</td>
		</tr>
		<tr>
			<td>
			3
			</td>
			<td>
			density
			</td>
			<td>
			Mass / volume
			</td>
			<td>
			[ML-3T0 ]
			</td>
			<td>
			Kg m-3
			</td>
		</tr>
		<tr>
			<td>
			4
			</td>
			<td>
			Speed or velocity
			</td>
			<td>
			Distance / time
			</td>
			<td>
			[M0LT-1 ]
			</td>
			<td>
			m s-1
			</td>
		</tr>
		<tr>
			<td>
			5
			</td>
			<td>
			accelerati on
			</td>
			<td>
			Change in velocity / time
			</td>
			<td>
			[M0LT-2 ]
			</td>
			<td>
			m s-2
			</td>
		</tr>
		<tr>
			<td>
			6
			</td>
			<td>
			momentu m
			</td>
			<td>
			Mass × velocity
			</td>
			<td>
			[MLT-1]
			</td>
			<td>
			Kg
			</td>
		</tr>
		<tr>
			<td>
			7
			</td>
			<td>
			force
			</td>
			<td>
			Mass × acceleration
			</td>
			<td>
			[MLT-2]
			</td>
			<td>
			N
			</td>
		</tr>
		<tr>
			<td>
			8
			</td>
			<td>
			work
			</td>
			<td>
			Force × distance
			</td>
			<td>
			[ML2T-2 ]
			</td>
			<td>
			J
			</td>
		</tr>
		<tr>
			<td>
			9
			</td>
			<td>
			energy
			</td>
			<td>
			Amount of work
			</td>
			<td>
			[ML2T-2 ]
			</td>
			<td>
			J
			</td>
		</tr>
		<tr>
			<td>
			10
			</td>
			<td>
			power
			</td>
			<td>
			Work / time
			</td>
			<td>
			[ML2T-3 ]
			</td>
			<td>
			W
			</td>
		</tr>
		<tr>
			<td>
			11
			</td>
			<td>
			pressure
			</td>
			<td>
			Force / area
			</td>
			<td>
			[ML-1T-2]
			</td>
			<td>
			Pa
			</td>
		</tr>
		<tr>
			<td>
			12
			</td>
			<td>
			Gravitation al constant ‘G’
			</td>
			<td>
			[Force × (distance)2] ÷ [mass × mass]
			</td>
			<td>
			[M-1L3T-2]
			</td>
			<td>
			Nm2kg-2
			</td>
		</tr>
		<tr>
			<td>
			13
			</td>
			<td>
			stress
			</td>
			<td>
			Force / area
			</td>
			<td>
			[ML-1T-2]
			</td>
			<td>
			Nm-2
			</td>
		</tr>
		<tr>
			<td>
			14
			</td>
			<td>
			strain
			</td>
			<td>
			Change in dimension / original dimension
			</td>
			<td>
			Dimensionle ss
			</td>
			<td>
			-
			</td>
		</tr>
		<tr>
			<td>
			15
			</td>
			<td>
			Coefficient of elasticity
			</td>
			<td>
			Stress / strain
			</td>
			<td>
			[ML-1T-2]
			</td>
			<td>
			Nm-2
			</td>
		</tr>
		<tr>
			<td>
			16
			</td>
			<td>
			angle
			</td>
			<td>
			Arc / radius
			</td>
			<td>
			Dimensionle ss
			</td>
			<td>
			-
			</td>
		</tr>
		<tr>
			<td>
			17
			</td>
			<td>
			angular velocity
			</td>
			<td>
			Angle / time
			</td>
			<td>
			[M0L0T-2]
			</td>
			<td>
			Rad s-1
			</td>
		</tr>
		<tr>
			<td>
			18
			</td>
			<td>
			Moment of inertia
			</td>
			<td>
			Mass × (distance)2
			</td>
			<td>
			[ML2T0]
			</td>
			<td>
			Kg m2
			</td>
		</tr>
		<tr>
			<td>
			19
			</td>
			<td>
			frequency
			</td>
			<td>
			1 / time period
			</td>
			<td>
			[M0L0T-1]
			</td>
			<td>
			s-1 or Hz
			</td>
		</tr>
		<tr>
			<td>
			20
			</td>
			<td>
			Plank&#39;s constant
			</td>
			<td>
			Energy / frequency
			</td>
			<td>
			[ML2T-1]
			</td>
			<td>
			Js
			</td>
		</tr>
		<tr>
			<td>
			21
			</td>
			<td>
			Relative density
			</td>
			<td>
			Density of substance / density of water
			</td>
			<td>
			Dimensionle ss
			</td>
			<td>
			-
			</td>
		</tr>
		<tr>
			<td>
			22
			</td>
			<td>
			Heat or enthalpy
			</td>
			<td>
			energy
			</td>
			<td>
			[ML2T-2]
			</td>
			<td>
			J
			</td>
		</tr>
		<tr>
			<td>
			23
			</td>
			<td>
			Thermal conductivit y
			</td>
			<td>
			(Heat × distance)

			/ (area × temp. × time)
			</td>
			<td>
			[MLT-3K-1]
			</td>
			<td>
			Js-1m-1 k-1
			</td>
		</tr>
		<tr>
			<td>
			24
			</td>
			<td>
			Universal gas constant
			</td>
			<td>
			PV/nT
			</td>
			<td>
			[ML2T-2K-1 mol-1]
			</td>
			<td>
			Jmol-1 k-1
			</td>
		</tr>
		<tr>
			<td>
			25
			</td>
			<td>
			Boltzman n&#39;s constant
			</td>
			<td>
			Energy / temperature
			</td>
			<td>
			[ML2T-2K-1]
			</td>
			<td>
			JK-1
			</td>
		</tr>
		<tr>
			<td>
			26
			</td>
			<td>
			Stefan&#39;s constant
			</td>
			<td>
			Energy / [area

			× time × (temp)2]
			</td>
			<td>
			[ML0T-3K-4]
			</td>
			<td>
			Js-1m-4 K-4
			</td>
		</tr>
		<tr>
			<td>
			27
			</td>
			<td>
			Electric charge
			</td>
			<td>
			Time × current
			</td>
			<td>
			[M0L0TA]
			</td>
			<td>
			C

			(coulom b)
			</td>
		</tr>
		<tr>
			<td>
			28
			</td>
			<td>
			Electric potential
			</td>
			<td>
			Work / charge
			</td>
			<td>
			[ML2T-3A-1]
			</td>
			<td>
			V (volt)
			</td>
		</tr>
		<tr>
			<td>
			29
			</td>
			<td>
			resistance
			</td>
			<td>
			Potential difference / current
			</td>
			<td>
			[ML2T-3A-2]
			</td>
			<td>
			Ω(ohm)
			</td>
		</tr>
		<tr>
			<td>
			30
			</td>
			<td>
			capacitan ce
			</td>
			<td>
			Charge / potential difference
			</td>
			<td>
			[M-1L-2T4A2]
			</td>
			<td>
			F (farad)
			</td>
		</tr>
		<tr>
			<td>
			31
			</td>
			<td>
			resistivity
			</td>
			<td>
			RA/l
			</td>
			<td>
			[ML3T-3A-2]
			</td>
			<td>
			m
			</td>
		</tr>
		<tr>
			<td>
			32
			</td>
			<td>
			Magnetic field
			</td>
			<td>
			F/[qv sinθ]
			</td>
			<td>
			[ML0T-2A-1]
			</td>
			<td>
			T (tesla)
			</td>
		</tr>
		<tr>
			<td>
			33
			</td>
			<td>
			Magnetic flux
			</td>
			<td>
			BA
			</td>
			<td>
			[ML2T-2A-1]
			</td>
			<td>
			Wb (weber)
			</td>
		</tr>
		<tr>
			<td>
			34
			</td>
			<td>
			Magnetic moment
			</td>
			<td>
			Current × area
			</td>
			<td>
			[M0L2T0A]
			</td>
			<td>
			Am2
			</td>
		</tr>
		<tr>
			<td>
			35
			</td>
			<td>
			Electric dipole moment
			</td>
			<td>
			q × 2l
			</td>
			<td>
			[M0LTA]
			</td>
			<td>
			Cm
			</td>
		</tr>
		<tr>
			<td>
			36
			</td>
			<td>
			conducta nce
			</td>
			<td>
			C = 1/R
			</td>
			<td>
			[M-1L-2T3A2]
			</td>
			<td>
			Ω-1 or mho
			</td>
		</tr>
		<tr>
			<td>
			37
			</td>
			<td>
			Mechanic al equivalent of heat
			</td>
			<td>
			W/H
			</td>
			<td>
			dimension less
			</td>
			<td>
			-
			</td>
		</tr>
		<tr>
			<td>
			38
			</td>
			<td>
			entropy
			</td>
			<td>
			Heat / temperature
			</td>
			<td>
			[ML2T-2K-1]
			</td>
			<td>
			JK-1
			</td>
		</tr>
	</tbody>
</table>

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