# Physics and Measurement   Share

## What is Physics and Measurement

Physics and measurements are mostly related to our day to day life activities. Physics is the branch of science which deals with the study of nature and its laws. For example, the orbiting of the moon around the earth, falling off an apple from a tree and tides in the sea on a full moon night can all be explained if we know Newton's law of gravitation and Newton's laws of motion. Physics is concerned with the basic rules which are applicable to various domains of life. We use measurement in our daily life and it makes easier for us to understand the basics about physical quantities.

Everyone is his life once must have gone to the market to purchase groceries and vegetables. Suppose you go to the market to buy potatoes, then the vegetable vendor will ask you how much quantity do you want and you tell him that you want 5 kg. This 5 kg is the mass of the potatoes. If you go to buy milk, you will buy it in liters. If you buy clothes, you buy those in meters. You will also study dimensional analysis to check for errors in equations. In this chapter, you will learn basic things about different fundamental/basic units that will help you understand other topics in physics clearly.

Prepare Online for JEE Main/NEET

Crack JEE 2021 with JEE/NEET Online Preparation Program

The mass can be measured using the weighing machine like this, Similarly, length can be measured using scale, measuring tapes, etc. We will be able to measure the size of an object and determine the units, dimensions, formulas of physical quantities. After measuring these values, we will learn about how to calculate errors in our measurement and we can check the accuracy of our calculations.

## Notes for Physics and Measurement

Now we will discuss the important topics along with an Overview of the chapter. After that, we will see the important formulas related to this chapter.

## Topics of Physics and Measurement

• Physical Quantities
• Fundamental and derived quantities
• System of units
• Practical Units
• Dimensions of physical quantities
• Dimensionless quantities
• Applications of dimensional analysis:-
1. Check the dimensional correctness
2. Conversion of one physical quantity into other
3. Derivation of new relations
• Significant figures,
• Errors of measurement.

## Overview Of Physics And Measurements

In physics and measurement, we will get to know about physical quantities and their different types. Here we will measure and compare the same kind of physical quantities with the help of numbers and units. These numbers and units together form a physical quantity. We all know that a car is much heavier than a bicycle but exactly how many times? This can be easily answered if we have chosen a standard mass and call it unit mass. If the car is 300 times heavier than the unit mass and the bicycle is 30 times, we will get to know that a car is 10 times heavier than the bicycle. Thus, the physical quantities are can be expressed in terms of a unit of that quantity.

The measurement of the quantity consists of two parts,i.e., the first part gives how many times of the standard unit and the second part represents the name of the unit. In this chapter, we will study standard units of fundamental physical quantities like length, time, mass, temperature and about derived quantities which can be expressed in terms of fundamental quantities. We will study about dimensional analysis of quantities and after that, we will be able to check whether the given formulas of any quantity are correct or not. Suppose you measure something and get an error in that measurement, then after studying this chapter you will be able to find the error in your measurements. You will learn how to find the dimensions of any derived physical quantities with the help of fundamental quantities. To denote dimensions we write it within the brackets.

For Example:- if we have to find the dimension of Force in terms of fundamental quantities, then we can derive it like this:-

As we know, F=ma

⇒[Force]= [mass]x[acceleration]

$\Rightarrow$[M]x[LT-2]=[MLT-2]

You will study about errors of measurement like absolute error, relative error, error in sum/product. For example, suppose there is a rod of length 6 cm and you are asked to measure the length of that rod using a scale. When you measure the length, it comes out to be 5.8 cm, then, in this case, the error is 6-5.8=0.2 cm. This is how you will calculate the error and there are also other methods to calculate the errors which you will learn in this chapter.

## Formulas for Physics And Measurements

1. Absolute Error for nth reading =$\Delta a_n= a_{n}- a_{m}$  = true value - measured value

2. Mean absolute error=$\dpi{100} \Delta\bar{ a}= \frac{\left | \Delta a_{1} \right |+\left | \Delta a_{2} \right |+....\left | \Delta a_{n} \right |}{n}$

3. Relative error=$Relative \ \ error=\frac{\Delta{ a}}{a_{m}}$

4. $Percentage \ \ error=\frac{\Delta{ a}}{a_{m}}\times100$%

5. Absolute error in sum (x=a+b) = $\Delta x= \pm \left ( \Delta a+\Delta b \right )$

6. Absolute error in difference (x=a-b)= $\Delta x= \pm \left ( \Delta a+\Delta b \right )$

7. Relative error in product (x=a.b)= $\frac{\Delta x}{x}= \pm \left ( \frac{\Delta a}{a} +\frac{\Delta b}{b} \right )$

8. Relative error in division (x = a/b)= $\frac{\Delta x}{x}= \pm \left ( \frac{\Delta a}{a} +\frac{\Delta b}{b} \right )$

## How to prepare for Physics And Measurements

First, you should have a basic idea about various measurement units of different physical quantities like length, mass, time. Also, you should have an idea about SI units and practical units like liters, ton, etc. which we use in our daily life. Please try to remember the most used formulas and units of quantities by practicing the questions and watching video lectures on each concept. Practice enough problems of finding dimensions, units, error measurement so that it becomes easy to remember different formulas.

How to Solve Questions of Physics and Measurements:

• Denote a basic/fundamental quantity by a particular symbol. For example- Mass is denoted by M, length by L, time by T. To find the dimension of a physical quantity, express that quantity in terms of basic quantities as the product of different powers of the basic quantities and the result that we obtain after the product is the dimension. Let’s understand this with the help of one example:

For example:-

Dimensions of      , where symbols  $\mu_0$ and $\epsilon _0$ have their usual meaning, are:

 a) b) c) d)

This can be solved using the relation of speed of light  . Therefore dimension of = dimension of = as dimension of speed (c) is

• And using the dimensions found, you can easily find the unit of quantities.

• One can also find the dimension of a physical constant like gravitational constant, Planck's constant by substituting the dimensions of physical quantities in a given equation.

• To check the dimensional correctness of physical relation, always check the dimensions of both sides of the equation and check that whether LHS=RHS or not. If yes, then that relation is dimensionally correct.

• To convert a physical quantity from one system to the other, use the concept that the measure of a physical quantity is always constant.

• To derive new relations or formulas for a physical quantity as a function of some fundamental quantities, assume that the physical quantity is proportional to basic quantities raised to some power and then equate all the quantities on both sides of the equation to find the values of the power.

You can solve all these questions with proper study and once you start solving examples of these topics. Always do the calculations with proper concentration and neatly to avoid getting confused.

## Tips for Physics and Measurement

1. This chapter mostly requires practicing and memorizing of formulas and units. You can also remember the dimensions if you practice enough questions.

2. Questions asked from this chapter are mostly related to finding dimensions, conversions and find errors in measurement.

3. Study the process of solving questions first and practice some examples. Don’t try to rush to solve practice problems.

4. Solve previous year question of various exam from this chapter.

5. Make a plan to prepare for this chapter and Stick to a Timetable.

Because as said by Carl Sandburg:

"Time is the most valuable coin in your life. You and you alone will determine how that coin will be spent. Be careful that you do not let other people spend it for you."

## Books for Physics and Measurement

For Physics and Measurements, you will find easy to moderate level questions in NCERT books, please solve them first. Then you can do questions from Understanding Physics by D.C. Pandey or H.C. Verma. Both of these books have good quality questions. But apart from these books, you should also give topic-wise online mock tests.

## Physics Chapter wise Notes For Engineering and Medical Exams

 Chapters No. Chapter Name Chapter 2 Kinematics Chapter 3 Laws of motion Chapter 4 Work Energy and Power Chapter 5 Rotational Motion Chapter 6 Gravitation Chapter 7 Properties of Solids and Liquids Chapter 8 Kinetic theory of Gases Chapter 9 Thermodynamics Chapter 10 Oscillations and Waves Chapter 11 Electrostatics Chapter 12 Current Electricity Chapter 13 Magnetic Effects of Current and Magnetism Chapter 14 Electromagnetic Induction and Alternating currents Chapter 15 Electromagnetic Waves Chapter 16 Optics Chapter 17 Dual Nature of Matter and Radiation Chapter  18 Atoms And Nuclei Chapter 19 Electronic devices Chapter 20 Communication Systems Chapter 21 Experimental skills

## How to prepare for Physics and Measurement for JEE Main

Most of the previous year's questions from this chapter are from dimensional formulae and dimensional analysis. This questions can be solved easily if the physics course is completed. No need for memorizing all dimensional formula. Dimensional formulae can be derived from basic equations easily. For example

Question- Dimensions of, $1/\mu _0\varepsilon _0$ where symbols have their usual meaning, are (AIEEE 2003)

 a) $L^{-1}T$ b) $L^{-2}T^{2}}$ c) $L^{2}T^{-2}$ d) $LT^{-1}$

This can be solved using:

The relation speed of light$C=\frac{1}{\sqrt{\mu_0\epsilon_0}}$ Therefor dimension of a $\mu_0\epsilon_0$ = dimension of =$C^2=L^2T^-^2$

• Another important section in this chapter is Errors In Measurement. This concept is used in the chapter Experimental Skills and in many problems from other chapters.

For Example- calculation of absolute error for a set of readings of the period of a simple pendulum etc.

Let's see another example from Errors

Question- The percentage of errors in quantities P, Q, R, and S are 0.5%, 1%, 3%, and 1.5%

respectively in the measurement of a physical quantity $A=\frac{P^3Q^2}{\sqrt{RS}}$
(JEE Main 2018)

The maximum percentage error in the value of A will be :

This can be solved using the concept :

Error in quantity raised to some power -$x=\frac{a^n}{b^m}\rightarrow \frac{\Delta x}{x}=\pm \left(n\frac{\Delta a}{a}+m\frac{\Delta b}{b}\right)$- wherein

$\bigtriangleup a$= absolute error in the measurement of a

$\bigtriangleup b$= absolute error in the measurement of b

$\bigtriangleup x$= absolute error in the measurement of x

$\frac{\Delta P}{P}100\%=0.5$        $\frac{\Delta Q}{Q}100\%=1$

$\frac{\Delta R}{R}100\%=3$           $\frac{\Delta S}{S}100\%=1.5$

$\frac{\Delta A}{A}100\%=3\frac{\Delta P}{P}100\%+2\frac{\Delta Q}{Q}100\%+1/2\frac{\Delta R}{R}100\%+\frac{\Delta S}{S}\times 100\%$

= $3\times 0.5+\2\times 1+1/2\times3+1.5= 6.5 %$$3\times 0.5+\2\times 1+1/2\times3+1.5= 6.5 \%$

• Significant figures is another topic from where the question is expected

For Example:

Question- The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 x 10-3 are

 a) 4, 4, 2 b) 5, 1, 2 c) 5, 1, 5 d) 5, 5, 2

Solution:

1)    23.023 has 5 significant digits (Any zeros between two significant digits are significant)

2)     0.0003 has only 1 significant digit as zero to the left of first non zero digits are not significant.

3) 2.1 x 10-3  It has two significant digits (A final zero or trailing zeros in the decimal portion ONLY are significant).

## TIPS

• Maximum Error in

1. Product x=a.b

Let $x=ab$

Then, $\frac{\bigtriangleup x}{x}=\pm\frac{\bigtriangleup a}{a}+\frac{\bigtriangleup b}{b}$

$\bigtriangleup x=$ absolute error in the measurement of x.
$\bigtriangleup a=$ absolute error in the measurement of a.
$\bigtriangleup b=$
absolute error in the measurement of b.

2. Error in difference (x=a-b)

Let    $x=a\pm b$,

Then $\bigtriangleup x=+\bigtriangleup a+\bigtriangleup b$

3. Error in division  x = a/b

$\frac{\bigtriangleup x}{x}=\pm\left ( \frac{\bigtriangleup a}{a}+\frac{\bigtriangleup b}{b} \right )$

4. Error in quantity raised to some power

$x=\frac{a^n}{b^m}\rightarrow \frac{\Delta x}{x}=\pm \left(n\frac{\Delta a}{a}+m\frac{\Delta b}{b}\right)$

## BOOKS

• For practice, any book for JEE Main preparation is enough.
• NCERT XI Part 1 book is the very helping and cost-saving resource for the students.
• Practice a more online test, for the online test you can visit learn.careers360.com

### Topics from Physics and Measurement

• Physics, Technology and Society ( JEE Main ) (1 concepts)
• S I Units ( JEE Main ) (16 concepts)
• Fundamental and Derived Units ( JEE Main ) (5 concepts)
• Dimensions of physical quantities, dimensional analysis and its applications ( JEE Main ) (26 concepts)
• Least Count, Accuracy and Precision of Measuring Instruments and Errors in Measurement ( JEE Main ) (20 concepts)
• Errors and Significant figures ( JEE Main ) (6 concepts)
• Physical quantities and units ( JEE Main ) (4 concepts)
• Dimension analysis and its application ( JEE Main ) (16 concepts)

Exams
Articles
Questions