SPACE AND TIME/UNIT AND DIMENSION

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