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JEE Important Chapter - Units And Measurement

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Important Concept of Units and Measurement for JEE

Important Concept of Units and Measurement for JEE

This chapter deals with the study of the physical world that surrounds us and various physical quantities that help us understand this world. It also tells us about what measurement is in physics. Basically, the process of determining the length, size, or amount of a thing is known as measurement. People have been measuring length in various ways since prehistoric times. 


A physical quantity (such as length) must be measured in relation to some fixed quantity. A unit is a set quantity against which a physical quantity is measured and it serves as a unit of measurement. There are three types of physical quantities like fundamental, derived and supplementary quantities. 


This chapter tells us about that there are four fundamental forces in nature and the name of them are:

  • Gravitational forces

  • Electromagnetic forces 

  • Strong nuclear forces

  • Weak nuclear forces


This chapter also deals with the dimensional analysis, error in measurement and tells us about the extent to which a physical measurement quantity is measured accurately through the concept of significant figures.


Now, let's move onto the important concepts and formulae related to JEE and JEE main exams along with a few solved examples.


Important Topics of Units and Measurement

  • Fundamental Forces in Nature

  • Dimensional Analysis

  • Accuracy, Precision and Error in Measurement

  • Error Arithmetic Operations of Significant Figures

  • Errors - Absolute Error, Relative Error,Percentage Error


Units and Measurement Important Concept for JEE

Name of the concept

Key points of the concepts

  1. Fundamental Forces in Nature

  • All the forces occurring in different contexts of the world are arise from a small number of fundamental forces and these are;

  • Gravitational Forces: It is the force of mutual attraction between any two objects by virtue of their mass.

$F=G\dfrac{m_1m_2}{r^2}$

  • Electromagnetic Forces: The force acting between two static electric charges is called electrostatic force and force acting between two magnetic poles is called magnetic  force. These forces are considered to be the two facets of a general force called electromagnetic force.

$F=G\dfrac{q_1q_2}{4\pi \epsilon r^2}$

  • Strong Nuclear Forces: The forces that bind the neutrons and protons together in the nucleus are known as strong nuclear forces.

  • Weak Nuclear Forces: These are the forces that appear only between elementary particles of short life times, involved in a nuclear process such as β - decay.

  1. Dimensional Analysis

  • The dimension of a physical quantity are the powers to which the units of base quantities are raised to represent a derived unit of that quantity.

  • The expression which shows how and which of the base quantities represents a physical quantity is called the dimension formula.

  • Dimensional analysis used for; conversion of one system of units into another, checking the correctness of formulas and in deriving the formulas.

  1. Accuracy, Precision and Error in Measurement

  • A measurement's accuracy is a measure of how near the measured value is to the quantity's real value.

  • Precision tells us to what resolution or limit, the quantity is measured by a measuring instrument.

  • The difference between the true value and the measured value of a quantity is known as error of measurement.

  1. Error Arithmetic Operations of Significant Figures

  • Significant Figure: The digits that are known reliably plus the first uncertain digit are known as significant digits or significant figures.

  • Some common rules have to be followed while counting the significant figures.

  1. Errors - Absolute Error, Relative Error, Percentage error

  • The magnitude of the discrepancy between the real value and the individual measured value of a physical quantity is known as absolute error in measurement.

  • Relative error is defined as the ratio of mean absolute error to the mean value of the quantity measured.

  • Percentage error is the difference between the estimated value and the actual value in respect to the actual value.


List of Important formulas for Units and Measurement 

S.No.

Name of the Concept

Formula


Dimensional Analysis

For conversion of one system of units into another.

$n_1=n_2[\dfrac{M_1}{M_2}]^a[\dfrac{L_1}{L_2}]^b[\dfrac{T_1}{T_2}]^c$



Errors - Absolute Error, Relative Error, Percentage error

Absolute Error, $Δa_n=a_m - a_n$

Relative Error, $δa=\dfrac{Δa_{mean}}{a_n}$

Here, $a_m$= True value, $a_n$ = individual measured value and $Δa_{mean}$ = mean absolute error.

Percentage Error, 

$δa=\dfrac{Δa_{mean}}{a_m} \times 100$


Combination of Errors

Error in sum: If $x=a+b$ then its maximum error in measurement is,

$\Delta x=\pm (\Delta a+\Delta b)$

Error in difference: If $x=a-b$ then its maximum error in measurement is,

$\Delta x=\pm(\Delta a+\Delta b)$

Error in product: If $x=ab$ then its maximum error in measurement is

$\dfrac{Δx}{x}= \pm (\dfrac{Δa}{a}+\dfrac{Δb}{b})$

Error in division: If x=a/b then its maximum error in measurement is

$\dfrac{Δx}{x}= \pm (\dfrac{Δa}{a}+\dfrac{Δb}{b})$



Solved Examples 

1. A student produces a positive error of 2% in the length of the pendulum and a negative error of 4% in the amount of time period while measuring the acceleration due to gravity with a pendulum. His percentage error in measurement g using the ratio $g=4\pi^2( \dfrac{l}{T^2})$ will be

  1. 6 %

  2. 8 %

  3. 10%

  4. 12% 

Sol:

Given that,

Percentage error in length, $\dfrac{\Delta l}{l}\times 100=2\%$

Percentage error in time period, $\dfrac{\Delta T}{T}\times 100=4\% $

The expression of acceleration due to gravity, $g=4\pi^2( \dfrac{l}{T^2})$

The percentage error in the measurement of g is given as,

$\dfrac{\Delta g}{g} \times 100= \dfrac{\Delta l}{l} \times 100 +2\times \dfrac{\Delta T}{T}\times 100$

After putting the values, we get

$\dfrac{\Delta g}{g}\times 100= 2\%+2\times 4\%=10\%$


Hence, the option c is correct.


Key point: The formula of percentage error and combinational error is important to solve this type of problem.


2. The potential energy of the particle varies with distance x as $U=\dfrac{Ax^{2/3}+B}{x^2}$, where A and B are constants. The dimensional formula for AB is 

  1. $[M^2 L^{19/3} T^{-4}]$

  2. $[M^2 L^{21/3} T^{-4}]$ 

  3. $[M^2 L^{20/3} T^{-4}]$

  4. $[M^2 L^{22/3} T^{-4}]$

Sol:

Given,

Potential energy, $U=\dfrac{Ax^{2/3}+B}{x^2}$

$U=$[M^1 L^2 T^{-2}]$

As $x$ is a distance hence its dimension is $[L]$.

Now using the principle of homogeneity of dimensional analysis, we can write;

$U=\dfrac{Ax^{2/3}}{x^2}$ and $U=\dfrac{B}{x^2}$

Now putting the dimensional formula of each quantity in the above equations we get:

$[M^1 L^2 T^{-2}]= A\dfrac{[L^{2/3}]}{[L^2]}=A [L^{-4/3}]$

We can also write,

$A=\dfrac{[M^1L^2 T^{-2}]}{[L^{-4/3}]}=[M^1 L^{10/3} T^{-2}]$

Similarly, 

$U=\dfrac{B}{x^2}$

After putting the dimensional formula of the quantities we get;

$[M^1 L^2 T^{-2}]=\dfrac{B}{[L^{2}]}$ 

We can also write,

$B=[M^1 L^2 T^{-2}][L^{2}]=[M^1 L^4 T^{-2}]$

As the dimensional formula of A and B is known, so in order to obtain

Dimensional formula of AB we can write;

$AB=[M^1 L^{10/3} T^{-2}][M^1 L^4 T^{-2}]=[M^2 L^{22/3} T^{-4}]$


Hence option d is correct.


Key point: Always use the principle of homogeneity of dimensional analysis to find the dimension of unknown quantity.


Previous Year Questions from JEE Paper

1. If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula $P=EL^2M^{-5}G^{-2}$ are :(JEE Main 2018)

  1. $[M^0 L^1 T^0]$

  2. $[M^{-1} L^{-1} T^{2}]$

  3. $[M^1 L^1 T^{-2}]$

  4. $[M^0 L^0 T^0]$

Sol:

Given the formula,$P=EL^2M^{-5}G^{-2}$  

So in order to find the dimension of P, we have to use the dimensional formula of quantities E, L, M and G which are energy, angular momentum, mass and constant of gravitation.

Dimensional Formula of energy, $E=[M^1 L^2 T^{-2}]$

Dimensional Formula of angular momentum,$L=[M^1 L^2 T^{-1}]$

Dimensional Formula of mass,$M=[M^1]$

Dimensional Formula for constant of gravitation,$G=[M^{-1} L^3 T^{2}]$ 

After putting the dimensional formula of all the quantities in the given formula we can obtain the dimension of P as,

$P=[M^1 L^2 T^{-2}][M^2 L^4 T^{-2}][M^{-5}][M^2 L^{-6} T^{4}]$

After adding and subtracting the powers of M,L and T, we get;

$P=[M^0 L^0 T^0]$


Hence, option d is correct.


Trick: Remembering the dimensional formula for various standard quantities like force, energy, momentum, moment of inertia etc is important to solve such a problem.


2. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then the error in the value of resistance of the wire is (JEE Main 2017)

  1. 3 %

  2. 6 %

  3. Zero

  4. 1 %

Sol:

Given that,

Percentage error in measurement of current, $\dfrac{\Delta I}{I}\times 100=3\%$

Percentage error in measurement of potential difference, $\dfrac{\Delta V}{V}\times 100=3\%$ 

We know that the formula of between potential difference and current is given as,

$V=IR$

And in the form of percentage error we can write the above relation as,

$\dfrac{\Delta V}{V}\times 100=\dfrac{\Delta I}{I}\times 100+\dfrac{\Delta R}{R}\times 100$

From the above relation the error in the measurement of resistance is given as,

$\dfrac{\Delta R}{R}\times 100=\dfrac{\Delta V}{V}\times 100+\dfrac{\Delta I}{I}\times 100$

After putting the values of known quantities we get;

$\dfrac{\Delta R}{R}\times 100= 3\%+3\%=6\%$


Hence error in the measurement of resistance is $6\%$. Therefore, option c is correct.


Trick: To solve such problems we need to have knowledge about the percentage error formula and combinational error.


Practice Questions

  1. The density of a substance in the shape of a cube is found by measuring the cube's three sides and mass. Calculate the maximum error in predicting density if the relative errors in measuring mass and length are 1.5% and 1%, respectively. (Ans: 4.5%)

  2. A copper wire is stretched to lengthen it by 0.5 percent. If its volume remains constant, the percentage change in its electrical resistance is ?(Ans: 1%)


Conclusion

In this article we have talked about the measurements, physical quantities and its various types, fundamental forces, various types of error in measurement and also get the answer about what is Units and measurement. Also provide the problem that helps us to understand the application of these concepts.

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27th June 2022 - exam-strategy
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24th July 2022 - Maths, Physics and Chemistry
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24th July 2022 - Maths, Physics and Chemistry
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25th July 2022 - Maths, Physics and Chemistry
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25th July 2022 - Maths, Physics and Chemistry
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27th July 2022 - Maths, Physics and Chemistry
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June, July
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JEE Main 2022 Book Solutions and PDF Download

JEE Main 2022 Book Solutions and PDF Download

View all JEE Main Important Books
In order to prepare for JEE Main 2022, candidates should know the list of important books i.e. RD Sharma Solutions, NCERT Solutions, RS Aggarwal Solutions, HC Verma books and RS Aggarwal Solutions. They will find the high quality readymade solutions of these books on Vedantu. These books will help them in order to prepare well for the JEE Main 2022 exam so that they can grab the top rank in the all India entrance exam.
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books
Maths
NCERT Book for Class 12 Maths
books
Physics
NCERT Book for Class 12 Physics
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JEE Main Mock Tests

JEE Main Mock Tests

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JEE Main 2022 free online mock test series for exam preparation are available on the Vedantu website for free download. Practising these mock test papers of Physics, Chemistry and Maths prepared by expert teachers at Vedantu will help you to boost your confidence to face the JEE Main 2022 examination without any worries. The JEE Main test series for Physics, Chemistry and Maths that is based on the latest syllabus of JEE Main and also the Previous Year Question Papers.
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JEE MAIN MOCK TEST - 1
3 hr  • 75 questions • OBJECTIVE
JEE MAIN MOCK TEST - 3
3 hr  • 75 questions • OBJECTIVE
JEE MAIN MOCK TEST - 2
3 hr  • 75 questions • OBJECTIVE
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Chemistry master teacher

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Luv Mehan

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JEE Main 2022 Cut-Off

JEE Main 2022 Cut-Off

JEE Main Cut Off
NTA is responsible for the release of the JEE Main 2022 June and July Session cut off score. The qualifying percentile score might remain the same for different categories. According to the latest trends, the expected cut off mark for JEE Main 2022 June and July Session is 50% for general category candidates, 45% for physically challenged candidates, and 40% for candidates from reserved categories. For the general category, JEE Main qualifying marks for 2021 ranged from 87.8992241 for general-category, while for OBC/SC/ST categories, they ranged from 68.0234447 for OBC, 46.8825338 for SC and 34.6728999 for ST category.
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JEE Main 2022 Results

JEE Main 2022 Results

JEE Main 2022 June and July Session Result - NTA has announced JEE Main result on their website. To download the Scorecard for JEE Main 2022 June and July Session, visit the official website of JEE Main NTA.
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Rank List
Counselling
Cutoff
JEE Main 2022 state rank lists will be released by the state counselling committees for admissions to the 85% state quota and to all seats in NITs and CFTIs colleges. JEE Main 2022 state rank lists are based on the marks obtained in entrance exams. Candidates can check the JEE Main 2022 state rank list on the official website or on our site.
The NTA will conduct JEE Main 2022 counselling at https://josaa.nic.in/. There will be two rounds of counselling for admission under All India Quota (AIQ), deemed and central universities, NITs and CFTIs. A mop-up round of JEE Main counselling will be conducted excluding 15% AIQ seats, while the dates of JEE Main 2022 June and July session counselling for 85% state quota seats will be announced by the respective state authorities.
NTA is responsible for the release of the JEE Main 2022 June and July Session cut off score. The qualifying percentile score might remain the same for different categories. According to the latest trends, the expected cut off mark for JEE Main 2022 June and July Session is 50% for general category candidates, 45% for physically challenged candidates, and 40% for candidates from reserved categories. For the general category, JEE Main qualifying marks for 2021 ranged from 87.8992241 for general category, while for OBC/SC/ST categories, they ranged from 68.0234447 for OBC, 46.8825338 for SC and 34.6728999 for ST category.
Want to know which Engineering colleges in India accept the JEE Main 2022 scores for admission to Engineering? Find the list of Engineering colleges accepting JEE Main scores in India, compiled by Vedantu. There are 1622 Colleges that are accepting JEE Main. Also find more details on Fees, Ranking, Admission, and Placement.
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Counselling

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FAQs on JEE Important Chapter - Units And Measurement

FAQ

1. What is the weightage of the Units and Measurement in JEE mains?

From this chapter approximately 1-2 questions are asked every year and thus leading to the approximate weightage of 2-3% in the exam.

2. What is the difficulty level of the questions asked from this chapter ?

As this chapter contains the most basic concepts of Physics, therefore the difficulty level of the questions asked from this chapter is from easy to moderate.

3. Is practicing previous year questions really helpful in this exam ?

In order to score well and be habitual with the difficulty level of the exam, we have to practice the previous year question. It not only boosts our self confidence but also gives exposure to the area of improvement. Solving past ten to fifteen year question papers helps in understanding the concept in a better way and also gives the idea about how many times a concept or topic gets repetitive in the exam. Practicing previous year questions also helps in preparing the Units and measurements jee note for better understanding.