Class 11 Exam > Class 11 Questions > as Sn=u+a/2(2n-1) have no dimensional homogen...
Start Learning for Free
as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..??
Verified Answer
as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely ...
Here, S=u+(1/2)*a*(2n-1) this equation is used to find distance travelled by body in nth second.
LHS
So, S(nth) = distance travelled in nth second
i.e S(nth) = [L]/[T] = [LT^-1] dimensionally
RHS
Now, U+(1/2)*a*(2n-1) = where,
U= initial velocity = [LT^-1]
a= acceleration = [LT^-2]
2n-1= n=time = [T]
1/2=dimensionless = [MdegreeLdegreeTdegee]
U+(1/2)*a*(2n-1)= [LT^-1]+[LT^-2]*[T]
[LT^-1]+[LT-^1]=[LT^-1] by principle of homogeneity.
As LHS= RHS dimensionally i.e [LT^-1]
Therefore, it is dimensionally correct.
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely ...
Introduction:
The formula Sn = u * (a/2) * (2n - 1) represents the sum of an arithmetic series. Here, Sn represents the sum of the series, u represents the first term, a represents the common difference, and n represents the number of terms.
Explanation of Dimensional Homogeneity:
Dimensional homogeneity refers to the consistency of units in a mathematical equation or formula. For an equation to be dimensionally homogeneous, the units on both sides of the equation should be the same.
In the given formula Sn = u * (a/2) * (2n - 1), the units can be analyzed as follows:
- Sn represents the sum of the series and has units of the first term u.
- u represents the first term of the series and has its own units.
- a represents the common difference between terms and has its own units.
- n represents the number of terms and is dimensionless.
Lack of Dimensional Homogeneity:
Upon analyzing the formula, it becomes evident that the units on both sides of the equation do not match. The left side of the equation, Sn, has units of the first term u, while the right side of the equation has a combination of u and a. Therefore, the formula Sn = u * (a/2) * (2n - 1) lacks dimensional homogeneity.
Widespread Use:
Despite the lack of dimensional homogeneity, the formula Sn = u * (a/2) * (2n - 1) is still widely used in the field of arithmetic series. This is because the formula provides a convenient way to calculate the sum of an arithmetic series, even though the units may not match.
While dimensional homogeneity is an important aspect of mathematical equations in physics, it does not necessarily determine the usability or validity of a formula. In some cases, formulas may lack dimensional homogeneity but still provide accurate results when used appropriately.
It is important to note that when using the formula Sn = u * (a/2) * (2n - 1), one should ensure that the units of the first term u and the common difference a are consistent. This means that both u and a should have the same units to avoid any inconsistencies in the calculations.
In Summary:
- The formula Sn = u * (a/2) * (2n - 1) lacks dimensional homogeneity as the units on both sides of the equation do not match.
- Despite lacking dimensional homogeneity, the formula is widely used in arithmetic series calculations.
- It is important to ensure that the units of the first term u and the common difference a are consistent when using the formula.
The formula Sn = u * (a/2) * (2n - 1) represents the sum of an arithmetic series. Here, Sn represents the sum of the series, u represents the first term, a represents the common difference, and n represents the number of terms.
Explanation of Dimensional Homogeneity:
Dimensional homogeneity refers to the consistency of units in a mathematical equation or formula. For an equation to be dimensionally homogeneous, the units on both sides of the equation should be the same.
In the given formula Sn = u * (a/2) * (2n - 1), the units can be analyzed as follows:
- Sn represents the sum of the series and has units of the first term u.
- u represents the first term of the series and has its own units.
- a represents the common difference between terms and has its own units.
- n represents the number of terms and is dimensionless.
Lack of Dimensional Homogeneity:
Upon analyzing the formula, it becomes evident that the units on both sides of the equation do not match. The left side of the equation, Sn, has units of the first term u, while the right side of the equation has a combination of u and a. Therefore, the formula Sn = u * (a/2) * (2n - 1) lacks dimensional homogeneity.
Widespread Use:
Despite the lack of dimensional homogeneity, the formula Sn = u * (a/2) * (2n - 1) is still widely used in the field of arithmetic series. This is because the formula provides a convenient way to calculate the sum of an arithmetic series, even though the units may not match.
While dimensional homogeneity is an important aspect of mathematical equations in physics, it does not necessarily determine the usability or validity of a formula. In some cases, formulas may lack dimensional homogeneity but still provide accurate results when used appropriately.
It is important to note that when using the formula Sn = u * (a/2) * (2n - 1), one should ensure that the units of the first term u and the common difference a are consistent. This means that both u and a should have the same units to avoid any inconsistencies in the calculations.
In Summary:
- The formula Sn = u * (a/2) * (2n - 1) lacks dimensional homogeneity as the units on both sides of the equation do not match.
- Despite lacking dimensional homogeneity, the formula is widely used in arithmetic series calculations.
- It is important to ensure that the units of the first term u and the common difference a are consistent when using the formula.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics
Question Description
as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics.
as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics.
Solutions for as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics defined & explained in the simplest way possible. Besides giving the explanation of
as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics, a detailed solution for as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics has been provided alongside types of as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics theory, EduRev gives you an
ample number of questions to practice as Sn=u+a/2(2n-1) have no dimensional homogenity then also its widely used..?? Related: Dimensions (Formulae and Equations) - Units and Measurements, Class 11, Physics tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup