
Derive the relation for conversion of one unit system to another using the dimensions.
Answer
411.3k+ views
Hint: In order to answer this question, to know the derivation of a given relation between two systems, we will take two systems of the physical quantities and then compare them by making their equations by their formula with their different units.
Complete step by step answer:
Conversion of physical quantity units from one system to another: When the value of a physical quantity in one system is known, the process of dimensional analysis may be used to determine its value in another system.
As discussed, the measurement of a physical quantity is given by:
$Q = nu$
If the unit of a physical quantity in a system is ${u_1}$ , and the numerical value is ${n_1}$ , then:
$Q = {n_1}{u_1}$ ……...…(i)
Similarly, in the other system if the unit is ${u_2}$ and magnitude is ${n_2}$ then:
$Q = {n_2}{u_2}$ ……...…..(ii)
From eq(i) and eq(ii):
${n_1}{u_1} = {n_2}{u_2}$ ……...……(iii)
If \[a,b,c\] are the dimensions of a physical quantity in mass, length and time in the two systems, then
${n_2}={n_1}{[\dfrac{{{M_1}}}{{{M_2}}}]^a}{[\dfrac{{{L_1}}}{{{L_2}}}]^b}{[\dfrac{{{T_1}}}{{{T_2}}}]^c}$
When the value of a physical quantity in the first system is determined, the equation can be used to find its value in the second or new system.
Note: A system of units is a set of similar units that are used in calculations. It includes both fundamental and derived units. Some units are used in many systems of measurement. The following are the various systems of units used to quantify physical quantities: The C.G.S (\[\text{Centimetre, Gram, Second}\]) unit system is a French system.
Complete step by step answer:
Conversion of physical quantity units from one system to another: When the value of a physical quantity in one system is known, the process of dimensional analysis may be used to determine its value in another system.
As discussed, the measurement of a physical quantity is given by:
$Q = nu$
If the unit of a physical quantity in a system is ${u_1}$ , and the numerical value is ${n_1}$ , then:
$Q = {n_1}{u_1}$ ……...…(i)
Similarly, in the other system if the unit is ${u_2}$ and magnitude is ${n_2}$ then:
$Q = {n_2}{u_2}$ ……...…..(ii)
From eq(i) and eq(ii):
${n_1}{u_1} = {n_2}{u_2}$ ……...……(iii)
If \[a,b,c\] are the dimensions of a physical quantity in mass, length and time in the two systems, then
${n_2}={n_1}{[\dfrac{{{M_1}}}{{{M_2}}}]^a}{[\dfrac{{{L_1}}}{{{L_2}}}]^b}{[\dfrac{{{T_1}}}{{{T_2}}}]^c}$
When the value of a physical quantity in the first system is determined, the equation can be used to find its value in the second or new system.
Note: A system of units is a set of similar units that are used in calculations. It includes both fundamental and derived units. Some units are used in many systems of measurement. The following are the various systems of units used to quantify physical quantities: The C.G.S (\[\text{Centimetre, Gram, Second}\]) unit system is a French system.
Recently Updated Pages
Questions & Answers - Ask your doubts

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Science: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Trending doubts
Write a book review which you have recently read in class 8 english CBSE

When people say No pun intended what does that mea class 8 english CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

Advantages and disadvantages of science

What is BLO What is the full form of BLO class 8 social science CBSE
