What is Motion in Two Dimensions ?
Motion in Two Dimensions An object moving in a plane is said to have two-dimensional motion. The two-dimensional motion is equal to the vector sum of two one-dimensional motions along the mutually perpendicular direction. Let the position of point $P$ at a time $t$ be given by position vector $\overrightarrow{\mathrm{OP}}=\overrightarrow{\mathrm{r}}$ $\vec{r}=\hat{i} r \cos \theta+\hat{j} r \sin \theta=\hat{i} x+\hat{j} y$ Also Read JEE Physics Notes To watch Free Learning Videos on JEE by Kota’...
Read More →How to derive the Formula by Dimensional Analysis method?
Derive the Formula by Dimensional Analysis method Let a physical quantity $x$ depends on the other quantity $P, Q$ and $R$. Then $x \propto(\mathrm{P})^{\mathrm{a}}(\mathrm{Q})^{\mathrm{b}}(\mathrm{R})^{\mathrm{c}}$ $x=\mathrm{k}(\mathrm{P})^{a}(\mathrm{Q})^{b}(\mathrm{R})^{c}$ Now consider dimensional formula of each quantity in both side - $a x_{1}+b x_{2}+c x_{3}=x$ ...(2) $a y_{1}+b y_{2}+c y_{3}=y$ ...(3) $a z_{1}+b z_{2}+c z_{3}=z$ ...(4) After solving equation $(2),(3)$ and $(4)$ value of...
Read More →How to check the Accuracy of a formula ?
To check the accuracy of a formula It is based on the homogeneity principle of dimension according to it formula is correct when L.H.S. $=$ R.H.S. Dimensionally. Ex. Test the correctness of the formula $\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$, where, $\mathrm{T}=$ time period $\ell=$ length of pendulum and $\mathrm{g}=$ Acc. due to gravity. Sol. L.H.S. Dimension Equation of $\mathrm{T} \Rightarrow \mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{1}$ R.H.S. Dimension equation of; $2 \pi \sqrt...
Read More →What are the Defects of Dimensional Analysis ?
Defects of Dimensional Analysis (i) While deriving a formula the proportionality constant cannot be found. (ii) The formula for a physical quantity depending on more than three other physical quantities cannot be derived. It can be checked only. (iii) The equations of the type $v=u \pm$ at cannot be derived. They can be checked only. (iv) The equations containing trigonometrical functions ( $\sin \theta, \cos \theta$, etc), logarithmic functions ( $\log x, \log x^{3}$ etc) and exponential functi...
Read More →What are the uses of Dimensional Equations? and what is Conversion of one system of units into another?
Uses of Dimensional Equations Following are the uses of dimensional equations. 1. Conversion of one system of units into another 2. Checking the accuracy of various formulas or equation 3. Derivation of Formula. Conversion of one system of units into another Let the numerical values are $n_{1}$ and $n_{2}$ of a given quantity $Q$ in two-unit system and the units are- $U_{1}=M_{1}^{a} L_{1}^{b} T_{1}^{c}$ and $U_{2}=M_{2}^{a} L_{2}^{b} T_{2}^{c}$ Therefore, By the principle $\mathrm{nu}=$ constan...
Read More →What is the principle of Homogeneity of Dimensions ?
Principle of Homogeneity of Dimensions The dimension of physical quantity on the left-hand side of the dimensional equation should equal to the net dimensions of all physical quantities on the right-hand side of it. Ex. If in the form $x=3 y z^{2}, x$ and $z$ represent electrical capacitances and magnetic induction the calculate the dimensional equation of $\mathrm{y}$. Sol. By the principle of homogeneity of dimension Dimension equation of $x \quad=$ Dimension equation of $\left(3 y z^{2}\right...
Read More →How to obtain dimensional formula of different Quantities ?
Dimensional formula of different Quantities Procedure : (i) Firstly we write the formula. (ii) Now change derived units in the fundamental units. (iii) At last solve the equation except for the given quantity. Note: Dimensionless quantity may have the unit. But unitless quantities are dimensionless. Ex. angle - dimensionless but it has unit radian. Also Read JEE Physics Notes To watch Free Learning Videos on JEE by Kota’s top IITian Faculties Install the eSaral App...
Read More →What is Dimensional Equation?
Dimensional Equation When a dimensional formula is equated to its physical quantity then the equation is called Dimensional Equation. Ex. Dimensional equation of Force : By $F=$ ma $\quad \Rightarrow \quad$ Dimension Equation of $F=\left[M^{1}\right]\left[L^{1} T^{-2}\right]=\left[M L T^{-2}\right]$ Ex. Dimensional equation of Energy : By $E=W=$ Force $\times$ Displacement Dimensional equation of ' $E$ ' $=\left[M^{1} L^{1} T^{-2}\right]\left[L^{1}\right]=\left[M^{1} L^{2} T^{-2}\right]$ Importa...
Read More →What are Dimensions of Physical Quantities ?
Dimensions of Physical Quantities The limit of a derived quantity in terms of necessary basic units is called dimensional formula and the raised powers on the basic units are dimensions. The basic units are represented as : Note : 1. A physical quantity may have a number of units but their dimensions would be same, Ex. The units of velocity are: $\mathrm{cms}^{-1}, \mathrm{~ms}^{-1}, \mathrm{~km} \mathrm{~s}^{-1}$. But the dimensional formula is $\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{1}$. ...
Read More →What is Classification of Unit System?
Classification of Unit System We have the following systems of the units: CGS system: This is the centimeter-gram-second system for the units of length, mass, and time respectively. FPS system: This is the foot-pound-second system for the units of length, mass and time respectively. MKS system: The MKS system of units is a physical system of measurement that uses the metre, kilogram, and second as base units. SI System: Also known as Systeme International d'Unites. This is a complete set of unit...
Read More →What are Derived Units ?
Derived Units The units of measurement derived from the seven base units specified by the International System of Units are known as SI derived units. They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation. The names of SI derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the s...
Read More →What are Fundamental Units?
Fundamental Units The units defined for the fundamental quantities are called fundamental units. * Triple Point of Water is the temperature at which ice, water and water vapours co-exist. Also Read JEE Physics Notes To watch Free Learning Videos on JEE by Kota’s top IITian Faculties Install the eSaral App...
Read More →What are Units and It's type?
What is Unit? Unit is the quantity of a constant magnitude which is used to measure the magnitudes of other quantities of the same nature. For the measurement of a physical quantity a definite magnitude of quantity is taken as standard and the name given to this standard is called unit. Properties of Unit (a) The unit should be well-defined. (b) The unit should be of some suitable size. (c) The unit should be easily reproducible. (d) The unit should not change with time. (e) The unit should not ...
Read More →What are physical quantities? and What are the Types of physical quantities?
What are Physical Quantities Those quantities which can describe the laws of physics and possible to measure are called physical quantities. A physical quantity is that which can be measured. Note: (1) There are also some physical quantities that are not completely specified even by magnitude, unit, and Direction. These physical quantities are called tensors. eg. moment of Inertia. (2) Physical quantity = Numerical value $\mathrm{x}$ unit Types of physical quantities The physical quantities whic...
Read More →Atomic Structure Handwritten Notes JEE PDF - Free PDF Download
Hey, are you a JEE Aspirants? and looking for ways to download Atomic Structure Handwritten Notes JEE PDF? If yes. Then read this post till the end. If you want to score high in your JEE exam then it is very important for you to understand and learn all topics of JEE Physics thoroughly. Handwritten Notes helps students to learn important concepts of subjects easily. JEE Physics Handwritten Notes provide detailed explanations of all the concepts that students can use to clear their doubts instant...
Read More →NCERT Exemplar Class 8 Science PDF Download - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science PDF? If yes. Then read this post till the end. NCERT Class 8 Science Syllabus includes lots of Important topics of Physics, Chemistry, and Biology such as Crop Production and Management, Materials: Metals and Non-Metals, Combustion and Flame, Friction, Sound, Pollution of Air and Water, etc. If you want to score high in your Class 8 Science exam then it is very important for you to understand and lear...
Read More →NCERT Exemplar Class 8 Science Chapter 18 - Pollution of Air and Water - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science Chapter 18 "Pollution of Air and Water"? If yes. Then read this post till the end. If you want to score high in your Class 8 Science exam then it is very important for you to understand and learn the topics of Class 8 Science thoroughly. In this article, we have listed NCERT Exemplars Class 8 Science Chapter 18 in PDF that you can download and start your Preparations easily. So, without wasting more t...
Read More →NCERT Exemplar Class 8 Science Chapter 17 - Stars and the Solar System - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science Chapter 17 "Stars and the Solar System"? If yes. Then read this post till the end. If you want to score high in your Class 8 Science exam then it is very important for you to understand and learn the topics of Class 8 Science thoroughly. In this article, we have listed NCERT Exemplars Class 8 Science Chapter 17 in PDF that you can download and start your Preparations easily. So, without wasting more t...
Read More →NCERT Exemplar Class 8 Science Chapter 16 - Light - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science Chapter 16 "Light"? If yes. Then read this post till the end. If you want to score high in your Class 8 Science exam then it is very important for you to understand and learn the topics of Class 8 Science thoroughly. In this article, we have listed NCERT Exemplars Class 8 Science Chapter 16 in PDF that you can download and start your Preparations easily. So, without wasting more time let’s start. NCER...
Read More →NCERT Exemplar Class 8 Science Chapter 15 - Some Natural Phenomena - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science Chapter 15 "Some Natural Phenomena"? If yes. Then read this post till the end. If you want to score high in your Class 8 Science exam then it is very important for you to understand and learn the topics of Class 8 Science thoroughly. In this article, we have listed NCERT Exemplars Class 8 Science Chapter 15 in PDF that you can download and start your Preparations easily. So, without wasting more time ...
Read More →NCERT Exemplar Class 8 Science Chapter 14 - Chemicals Effects of Electric Current - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science Chapter 14 "Chemicals Effects of Electric Current"? If yes. Then read this post till the end. If you want to score high in your Class 8 Science exam then it is very important for you to understand and learn the topics of Class 8 Science thoroughly. In this article, we have listed NCERT Exemplars Class 8 Science Chapter 14 in PDF that you can download and start your Preparations easily. So, without was...
Read More →NCERT Exemplar Class 8 Science Chapter 13 - Sound - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science Chapter 13 "Sound"? If yes. Then read this post till the end. If you want to score high in your Class 8 Science exam then it is very important for you to understand and learn the topics of Class 8 Science thoroughly. In this article, we have listed NCERT Exemplars Class 8 Science Chapter 13 in PDF that you can download and start your Preparations easily. So, without wasting more time let’s start. NCER...
Read More →Class 12 Physics Handwritten Notes PDF Chapter 7 - Alternating current - Free PDF Download
Hey, are you a class 12 student? and looking for ways to download Class 12 Physics Handwritten Notes PDF Chapter 7 "Alternating current"? If yes. Then read this post till the end. If you want to score high in your Class 12 Science exam then it is very important for you to understand and learn the all topics of Class 12 Physics thoroughly. Handwritten Notes helps students to learn important concepts of subjects easily. Class 12 Physics Handwritten Notes provide detailed explanations of all the co...
Read More →NCERT Exemplar Class 8 Science Chapter 12 - Friction - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science Chapter 12 "Friction"? If yes. Then read this post till the end. If you want to score high in your Class 8 Science exam then it is very important for you to understand and learn the topics of Class 8 Science thoroughly. In this article, we have listed NCERT Exemplars Class 8 Science Chapter 12 in PDF that you can download and start your Preparations easily. So, without wasting more time let’s start. N...
Read More →NCERT Exemplar Class 8 Science Chapter 11 - Force and Pressure - Free PDF Download
Hey, are you a class 8 student? and looking for ways to download NCERT Exemplar Class 8 Science Chapter 11 "Force and Pressure? If yes. Then read this post till the end. If you want to score high in your Class 8 Science exam then it is very important for you to understand and learn the topics of Class 8 Science thoroughly. In this article, we have listed NCERT Exemplars Class 8 Science Chapter 11 in PDF that you can download and start your Preparations easily. So, without wasting more time let’s...
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