<< Chapter < Page Chapter >> Page >

Conversion from one system to another

We note that same physical quantity is expressed in different units. Clearly, conversion of unit is associated with single physical quantity. We know that different units for physical quantities have evolved through human progress in different parts of the world and have prevailed despite efforts towards uniform system. Secondly, a physical quantity has different scales of measurement - small, large etc. Whatever be the reason of different units being used, we need to have a “conversion factor” which coverts one unit to another. The conversion related to magnitude of unit is defined by the system of measurement itself. For example, 1 kilogram is equal to 1000 gm. Here, we shall derive a process to affect the conversion of one unit of one kind to another kind. In another words, we shall derive a “dimensionless constant” as conversion factor.

The underlying principle of process involved here is that a given physical quantity has same dimensional constitution – whatever be the system or unit. This fact is underlined by the fact that a given quantity of a given physical entity remains same. For, example, whether we call 1 inch or 2.54 cm, the length remains same. Now, physical quantity is product of “measurement” and “unit. Hence, We know that :

Q = n 1 u 1 = n 2 u 2

Since unit represents a standard division of the quantity, the dimensional formula of the unit quantity is same as that of the quantity in question. Let dimensions of units in two systems are :

u 1 = [ M 1 a L 1 b T 1 c ]

u 2 = [ M 2 a L 2 b T 2 c ]

Combining equations, we have :

n 1 [ M 1 a L 1 b T 1 c ] = n 2 [ M 2 a L 2 b T 2 c ]

n 2 = [ M 1 a L 1 b T 1 c ] [ M 2 a L 2 b T 2 c ] n 1

This is the formula used to convert a quantity from one system of units to another. In case, only 1 unit of the quantity in first system is involved, then we can put n 1 = 1 in the above equation.

Problem : Convert 1 Joule in SI system into ergs in “cgs” system

Solution : Putting n 1 = 1 and applying formula, we have :

n 2 = [ M 1 a L 1 b T 1 c ] [ M 2 a L 2 b T 2 c ]

Now, the dimensional formula of energy is [ M L 2 T - 2 ] . Hence, a = 1, b = 2 and c = -2. Putting values in the equation and rearranging,

n 2 = [ 1 k g 1 g m ] 1 X [ 1 m 1 c m ] 2 X [ 1 s 1 s ] - 2

The basic units of SI system is related to corresponding basic units in “cgs” system as :

1 K g = 10 3 g m

1 m = 10 2 c m

1 s = 1 s

Putting in the conversion formula, we have :

n 2 = [ 10 3 g m 1 g m ] 1 X [ 10 2 c m 1 c m ] 2 X [ 1 s 1 s ] - 2

n 2 = 10 3 X 10 4 = 10 7

Hence,

1 J = 10 7 e r g s

Got questions? Get instant answers now!

Dimensional analysis

Dimensional analysis is based on the simple understanding of the fact that only similar quantities can be added, subtracted and equated. Can we add 2 mangoes and 3 oranges? This requirement of similar terms is the underlying principle of dimensional analysis. This principle is known as principle of homogeneity.

Dimensional analysis gives an insight into the composition of a physical quantity. Take the case of frequency. Its SI unit is Hertz. What is its true relation with basic quantities? Notwithstanding the exact definition, its dimensional formula tells us that it is actually inverse of time (T). It has the dimension of “-1” in time.

In this section, we shall discuss three important applications of dimensional analysis involving : (i) Transcendental functions (ii) checking of dimensional formula and (iii) derivation of a formula.

Questions & Answers

A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
58asagravitasnal firce
Amar
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58
sajjad
what is the definition of resolution of forces
Atinuke Reply
what is energy?
James Reply
Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form
Abdul
motion
Mustapha
highlights of atomic physics
Benjamin
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
أوك
عباس
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply

Get the best Physics for k-12 course in your pocket!





Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for k-12' conversation and receive update notifications?

Ask