Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
In order to make the measurement of a physical quantity we have, first of all, to evolve a standard for that measurement so that different measurements of same physical quantity can be expressed relative to each other. That standard is called a unit of that physical quantity.
(a) C.G.S (Centimeter-Grand-Second) system.
(b) F.P.S. (Foot-Pound-Second) system.
(c) M.K.S. (Meter-Kilogram--Second) system.
(d) M.K.S.A. (Meter-Kilogram-Second-Ampere) unit.
Dimensional formula of a physical quantity is the formula which tells us how and which of the fundamental units have been used for the measurement of that quantity.
(a) Write the formula for that quantity, with the quantity on L.H.S. of the equation.
(b) Convert all the quantities on R.H.S. into the fundamental quantities mass, length and time.
(c) Substitute M, L and T for mass, length and time respectively.
(d) Collect terms of M,L and T and find their resultant powers (a,b,c) which give the dimensions of the quantity in mass, length and time respectively.
(a) Dimensions of a physical quantity are independent of the system of units.
(b) Quantities having similar dimensions can be added to or subtracted from each other.
(c) Dimensions of a physical quantity can be obtained from its units and vice-versa.
(d) Two different physical quantities may have same dimensions.
(e) Multiplication/division of dimensions of two physical quantities (may be same or different) results in production of dimensions of a third quantity.
PHYSICAL QUANTITY
SYMBOL
DIMENSION
MEASUREMENT UNIT
UNIT
Length
s
L
Meter
m
Mass
M
Kilogram
Kg
Time
t
T
Second
Sec
Electric charge
q
Q
Coulomb
C
luminous intensity
I
Candela
Cd
Temperature
K
Kelvin
oK
Angle
none
Radian
None
Mechanical Physical Quantities (derived)
Area
A
L2
square meter
m2
Volume
V
L3
cubic meter
m3
velocity
v
L/T
meter per second
m/sec
angular velocity
w
T-1
radians per second
1/sec
acceleration
a
LT-2
meter per square second
m/sec2
angular acceleration
T-2
radians per square
second
1/sec2
Force
F
MLT-2
Newton
Kg m/sec2
Energy
E
ML2T-2
Joule
Kg m2/sec2
Work
W
Heat
Torque
Newton meter
Power
P
ML2T-3
watt or joule/sec
Kg m2/sec3
Density
D or ρ
ML-3
kilogram per
Kg/m3
pressure
ML-1T-2
Newton per square meter
Kg m-1/sec2
impulse
J
MLT-1
Newton second
Kg m/sec
Inertia
ML2
Kilogram square meter
Kg m2
luminous
flux
f
lumen (4Pi candle for point source)
cd sr
illumination
CL-2
lumen per
cd sr/m2
entropy
S
ML2T-2K-1
joule per degree
Kg m2/sec2K
rate of flow
L3T-1
per second
m3/sec
kinematic
viscosity
n
L2T-1
m2/sec
dynamic
ML-1T-1
per square meter
Kg/m sec
specific
weight
g
ML-2T-2
per cubic meter
Kg m-2/sec2
Electrical Physical Quantities (derived)
Electric
current
QT-1
Ampere
C/sec
emf, voltage,
potential
ML2T-2Q-1
Volt
Kg m2/sec2C
resistance or
impedance
R
ML2T-1Q-2
ohm
Kgm2 /secC2
conductivity
M-2L-2TQ2
mho
secC2/Kg m3
capacitance
M-1L-2T2 Q2
Farad
sec2C2/Kgm2
inductance
ML2Q-2
Henry
Kg m2 /C2
Current density
QT-1L-2
ampere per
C/sec m2
Charge density
r
QL-3
coulomb per cubic meter
C/m3
magnetic flux,
Magnetic induction
B
MT-1Q-1
weber per
Kg/sec C
magnetic
intensity
H
QL-1T-1
ampere per meter
C/m sec
magnetic vector
MLT-1Q-1
weber/meter
Kg m/sec C
field intensity
MLT-2Q-1
volt/meter or
newton/coulomb
Kg m/sec2 C
Electric displacement
D
QL-2
coulomb per square meter
C/m2
permeability
MLQ-2
henry per meter
Kg m/C2
permittivity,
e
T2Q2M-1L-3
farad per meter
sec2C2/Kgm3
dielectric constant
M0L0T0
frequency
f or n
Hertz
sec-1
angular frequency
Wave length
l
Meters
Principle of homogeneity:-
It states that “ the dimensional formulae of every term on the two sides of a correct relation must be same.”
Types of error:-
(a) Constant errors:- An error is said to be constant error if it affects, every time, a measurement in a similar manner.
(b) Systematic errors:- Errors which come into existence by virtue of a definite rule, are called systematic errors.
(c) Random error or accidental error:- Error which takes place in a random manner and cannot be associated with a systematic cause are called random or accidental errors.
(d) Absolute error:-
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Solved Examples on Unit and Dimensions Problem 1:-...