JEE Physics/ Lakshmikanta Satapathy/ Table of Units and Dimensional Formulae with the related Key equations necessary to determine the units and dimensions of Fundamental and Derived Physical quantities

1. Physics Helpline
L K Satapathy
Units and Dimensions
Units Dimensions Error 3
of
Physical Quantities
Mechanical Quantities in [ M L T ]
Thermal Quantities in [ M L T K ]
Electrical Quantities in [ M L T A ]

2. Physics Helpline
L K Satapathy Units Dimensions Error 3
Fundamental Quantities
1 0 0
[ ]M L T01 Mass Fundamental Kilogram
Sl. No Physical Quantity Equation Unit Dimensions
0 1 0
[ ]M L T02 Length Fundamental Meter
0 0 1
[ ]M L T03 Time Fundamental Second
0 0 0 1
[ ]M L T A
04
Electric current Fundamental Ampere
0 0 0 1
[ ]M L T K
05
Temperature Fundamental Kelvin

3. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
0 1 1
[ ]M L T 
06 Velocity
Sl. No Physical Quantity Equation Unit Dimensions
0 1 2
[ ]M L T 
07 Acceleration
1 1 1
[ ]M L T 
08 Momentum
1 1 2
[ ]M L T 
09 Force Newton
1 2 2
[ ]M L T 
10 Work Joule
v S t
1
.m s
a v t 2
.m s
.p mv
1
. .kg m s
.F m a
.W F S

4. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
1 2 3
[ ]M L T 
11 Power
Sl. No Physical Quantity Equation Unit Dimensions
1 1 2
[ ]M L T 
12 Pressure
1 1 1
[ ]M L T 
13 Impulse
1 2 2
[ ]M L T 
14 Torque
1 3 0
[ ]M L T
15 Density
Pascal
W t Watt
F A
.F t .N s
.F r
Mass vol
.N m
3
.kg m

5. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
1 1 2
[ ]M L T 
16 Stress
Sl. No Physical Quantity Equation Unit Dimensions
17 Strain
1 1 2
[ ]M L T 
18 Elastic Modulus
1 0 2
[ ]M L T 
19 Force const
1 2 2
[ ]M L T 20 P E , K E
Stress / Strain
F A
L L
2
.N m
F L
21,
2
mgh mv
Unitless Dimensionless
2
.N m
Joule
1
.N m

6. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
0 0 1
[ ]M L T 
21 Velocity gradient
Sl. No Physical Quantity Equation Unit Dimensions
22 Rate of flow
1 0 2
[ ]M L T 
23 Surface Tension
1 0 2
[ ]M L T 
24 Surface energy
25 Coeff of friction
Volume /time
Work / Area
v L
1
s
F L
F R 
2
.J m
1
.N m
3 1
.sm  0 3 1
[ ]M L T 
Unitless Dimensionless

7. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
26 Angle
Sl. No Physical Quantity Equation Unit Dimensions
27 Angular velocity
0 0 2
[ ]M L T 
28 Angular acceleration
1 2 1
[ ]M L T 
29 Angular momentum
30 Frequency
l r 
t 
t 
1f T
2 1
. .kg m s
0 0 1
[ ]M L T 
L mvR
Hertz
DimensionlessRadian
Radian/sec
Radian/sec2
0 0 1
[ ]M L T 

8. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
31 Areal velocity
Sl. No Physical Quantity Equation Unit Dimensions
32 Angular wave number
1 3 2
[ ]M L T 
33 Gravitational const.
0 1 2
[ ]M L T 
34 Gravitational Field
35 Gravitational Potential
Force/mass
Energy/mass
Area/time
2k  
2 2
G FR M
1
.N kg
0 1 0
[ ]M L T
0 2 2
[ ]M L T 
2 1
.m s 0 2 1
[ ]M L T 
1
m
2 2
. .N m kg
1
.J kg

9. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
36 Moment of inertia
Sl. No Physical Quantity Equation Unit Dimensions
37 Coeff of viscosity
1 1 1
[ ]M L T
38 Fluidity
0 2 1
[ ]M L T 
39 Kinematic viscosity
40 Planck’s const (h)
Deca poise
2
I MR
6F rv
1 
2 1
.m s
1 1 1
[ ]M L T 
1 2 1
[ ]M L T 
2
.kg m
1 2 0
[ ]M L T
1
( )Deca poise 
.J s
 
E h f

10. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
41 Thermal capacity
Sl. No Physical Quantity Equation Unit Dimensions
42 Coeff of thermal
conductivity
43 Gas Constant (R)
44 Specific heat
45 Stefan’s const ()
Q ms
Q kA t d
PV nT
2 4
. .W m K 
1
.J K 1 2 2 1
[ ]M L T K 
1 1
. .J K mol 
4
E T
1 1
. .W m K  1 1 3 1
[ ]M L T K 
1 2 2 1
[ ]M L T K 
s Q m 1 1
. .J Kg K  0 2 2 1
[ ]M L T K 
1 0 3 4
[ ]M L T K 

11. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
46 Electric Charge
Sl. No Physical Quantity Equation Unit Dimensions
47 Electric Field
48 Electric Flux
49 Potential Difference
50 Potential Gradient
Q I t
E F q
.E E A 
1
.V m
0 0 1 1
[ ]M L T A
V L
1
.N C 1 1 3 1
[ ]M L T A 
1 3 3 1
[ ]M L T A 
.V E L
Coulomb
2 1
. .N m C
Volt 1 2 3 1
[ ]M L T A 
1 1 3 1
[ ]M L T A 

12. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
51 Line charge density
Sl. No Physical Quantity Equation Unit Dimensions
52 Surface charge density
53 Volume charge density
54 Capacitance
55 Permittivity ()
q L 
2 1 2
. .C N m 
0 1 1 1
[ ]M L T A
2 2
4F q r
C q V Farad 1 2 4 2
[ ]M L T A 
1 3 4 2
[ ]M L T A 
1
.C m
q A  2
.C m 0 2 1 1
[ ]M L T A
0 3 1 1
[ ]M L T A3
.C m
q vol 

13. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
56
Resistance
Sl. No Physical Quantity Equation Unit Dimensions
57
Resistivity
58
Current density
59
Electrical Conductivity60
Conductance
J I A 0 2 0 1
[ ]M L T A
RA L 
1 3 3 2
[ ]M L T A 
2
.A m
R V I 
1 2 3 2
[ ]M L T A 
1
1 R
1 
1 2 3 2
[ ]M L T A 
.m
1 1
.m 

1 3 3 2
[ ]M L T A 

14. Physics Helpline
L K Satapathy Units Dimensions Error 3
Derived Quantities
61
Magnetic Flux
Sl. No Physical Quantity Equation Unit Dimensions
62
Inductance ( L )
63
Magnetic Induction
64
Inductive Reactance65
Magnetic Permeability
B F qv
1 0 2 1
[ ]M L T A 
LX L
Tesla
BA B Weber
1
. .T m A
2B I r

1 2 2 1
[ ]M L T A 
1 1 2 2
[ ]M L T A 
1 2 2 2
[ ]M L T A 
1 2 3 2
[ ]M L T A 
.L I B
1
.Wb A

15. Physics Helpline
L K Satapathy
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