UNIT AND DIMENSIONS

5. DIMENSIONAL FORMULAR

1.5 DIMENSIONAL FORMULAE

Dimensional Formula: An expression along with the power of mass, length & time which indicates how physical quantity depends upon fundamental physical quantity.

e.g.          Speed = Distance/Time

= [L¹]/[T¹] =[M⁰L¹T^-1]

It tells us that speed depends upon L & T. It does not depend upon M.

1.5.1 Dimensional Equation: An equation obtained by equating the physical quantity with its dimensional formula is called a dimensional equation.

The dimensional equation of area, density & velocity are given as under- Area = [M⁰L²T⁰]

Density = [M¹L^-3T⁰] Velocity = [M⁰L¹T^-1]

Dimensional formula SI& CGS unit of Physical Quantities

 

Sr. No.	Physical Quantity	Formula	Dimensions	Name of S.I unit
1	Force	Mass × acceleration	[M1L1T-2]	Newton (N)
2	Work	Force × distance	[M1L2T-2]	Joule (J)
3	Power	Work / time	[M1L2T-3]	Watt (W)
4	Energy ( all form )	Stored work	[M1L2T-2]	Joule (J)
5	Pressure, Stress	Force/area	[M1L-1T-2]	Nm-2
6	Momentum	Mass × velocity	[M1L1T-1]	Kgms-1
7	Moment of force	Force × distance	[M1L2T-2]	Nm
8	Impulse	Force × time	[M1L1T-1]	Ns
9	Strain	Change in dimension / Original dimension	[M0L0T0]	No unit
10	Modulus of Elasticity	Stress / Strain	[M1L-1T-2]	Nm-2
11	Surface energy	Energy / Area	[M1L0T-2]	Joule/m2
12	Surface Tension	Force / Length	[M1L0T-2]	N/m
13	Co-efficient of Viscosity	Force × Distance/ Area × Velocity	[M1L-1T-1]	N/m2
14	Moment of inertia	Mass  ×  (radius  of gyration)2	[M1L2T0]	Kg-m2
15	Angular Velocity	Angle / time	[M0L0T-1]	Rad.per sec
16	Frequency	1/Time period	[M0L0T-1]	Hertz
17	Area	Length × Breadth	[M0L2T0]	Metre2
18	Volume	Length × breadth × height	[M0L3T0]	Metre3
19	Density	Mass/ volume	[M1L-3T0]	Kg/m3
20	Speed or velocity	Distance/ time	[M0L1T-1]	m/s
21	Acceleration	Velocity/time	[M0L1T-2]	m/s2
22	Pressure	Force/area	[M1L-1T-2]	N/m2

Assignment

Instructions: This Assignment is to be done and submitted on or before 13th October, 2025.

1.  Into how many categories is physical quantity classified based on dimensional analysis, explain? 

2. Derive the dimensional formula of following Quantity & write down their dimensions.

(i)   Density  

(ii) Power

(iii) Co-efficient of viscosity  

(iv) Angle

3. Explain which of the following pair of physical quantities have the same dimension:

 (i) Work &Power (ii) Stress & Pressure (iii) Momentum &Impulse