# CBSE Class 11th Dimensional formulae and dimensional equations Details & Preparations Downloads

In the intricate world of physics, the concepts of dimensional formulae and dimensional equations play a crucial role. They are indispensable tools that not only help in understanding physical quantities but also aid in solving complex problems and verifying the consistency of equations.

**What are Dimensional Formulae?**

Dimensional formulae are expressions that represent the dimensions of physical quantities in terms of the fundamental dimensions of mass (M), length (L), and time (T). Each measurable quantity can be uniquely expressed as a combination of these fundamental dimensions.

**Example: **The dimensional formula for velocity is [M^0 L^1 T^-1], indicating zero dependence on mass, one on length, and a power of -1 on time.

**Basics of Dimensional Equations: **

Dimensional equations are derived from dimensional formulae and are used to check the consistency of physical equations. A dimensional equation is obtained by equating the dimensions of different terms in an equation.

**Example: **In the equation F = ma, where F is force, m is mass, and a is acceleration, the dimensional equation is [MLT^-2] = [M^1 L^1 T^-2], ensuring consistency on both sides.

**Applying Dimensional Analysis: **

Dimensional analysis is a powerful method for solving physics problems. By examining the dimensions of quantities involved, one can predict relationships between variables, perform unit conversions, and validate mathematical expressions.

**Example:** Using dimensional analysis, we can derive the formula for the period of a simple pendulum:

T= 2π √g L , where T is the period, L is the length, and g is the acceleration due to gravity.

**Dimensional Consistency:**

Ensuring dimensional consistency is crucial for validating equations. If the dimensions on both sides of an equation are not consistent, it suggests an error in the formulation.

**Example:** In the equation E=mc2, the dimensions on both sides are [ML^2T^-2], ensuring dimensional consistency.

**Common Dimensionless Ratios: **

Certain ratios formed by dividing physical quantities are dimensionless. These dimensionless ratios often reveal important insights into the physics of a system.

**Example:** The Reynolds number, a dimensionless quantity used in fluid mechanics, is given by

Re = Viscous Forces / Inertial Forces.

**What are Dimensional equations ?**

Dimensional equations are equations obtained by equating the dimensions of different physical quantities. These equations are crucial in dimensional analysis and play a significant role in verifying the consistency of mathematical expressions and equations. Here are a few examples of dimensional equations:

**1. Force Equation :**

The equation for force (F) is given by F=ma, where m is mass and a is acceleration. The dimensional equation for force is:

[F]=[M]⋅[L]⋅[T]−2

** 2. Work-Energy Equation:**

The work-energy equation is W=F⋅d, where W is work, F is force, and d is displacement. The dimensional equation for work is:

[W]=[F]⋅[L]

**3. Simple Harmonic Motion (SHM) Equation:**

The equation for the period (T) of a simple harmonic oscillator is

T=2π k / m , where m is mass and k is the spring constant. The dimensional equation for period is:

[T]=[M]−1/2⋅[L]1/2⋅[T]0

**4. Pendulum Period Equation:**

The period (T) of a simple pendulum is given by T=2π g L , where L is length and g is the acceleration due to gravity. The dimensional equation for the period of a pendulum is:

[T]=[l]1/2⋅[T]−1/2

**5. Einstein's Mass-Energy Equivalence Equation:**

Einstein's equation E=mc2 relates energy (E), mass (m), and the speed of light (c). The dimensional equation for energy is:

[E]=[M]⋅[L]2⋅[T]−2

**CBSE Class 11th Downloadable Resources: **

1. CBSE Class 11th Topic Wise Summary | View Page / Download |

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4. CBSE Class 11th Exemplar | View Page / Download |

5. CBSE Class 11th Previous Year Papers | View Page / Download |

6. CBSE Class 11th Sample Papers | View Page / Download |

7. CBSE Class 11th Question Bank | View Page / Download |

8. CBSE Class 11th Topic Wise Revision Notes | View Page / Download |

9. CBSE Class 11th Last Minutes Preparation Resources | View Page / Download |

10. CBSE Class 11th Best Reference Books | View Page / Download |

11. CBSE Class 11th Formula Booklet | View Page / Download |

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**SAMPLE PRACTICE QUESTIONS OF SIGNIFICANT FIGURES :**

**Q1. What is the Dimensional Formula of a Physical Quantity?**

Answer: The dimensional formula of a physical quantity is an expression that shows how and which of the base quantities represent the given quantity. It is obtained by expressing the quantity in terms of the base quantities using the algebraic symbols.

**Q2. Why are Dimensional Formulae Important?**

Answer: Dimensional formulae provide insights into the nature of physical quantities and their relationships. They help in checking the dimensional consistency of equations, deriving formulas, and understanding the dependence of a physical quantity on fundamental dimensions.

**Q3. What are the Seven Base Dimensions in the MKS System?**

Answer: The seven base dimensions in the MKS (meter-kilogram-second) system are length (L), mass (M), time (T), electric current (I), temperature (Θ), amount of substance (N), and luminous intensity (J).

**Q4. How is the Dimensional Formula Represented?**

Answer: The dimensional formula of a physical quantity is represented using square brackets and the symbols of the base dimensions. For example, the dimensional formula of velocity (v) is [LT⁻¹] (representing length divided by time).

**Q5. Can Dimensional Formulae be Used to Derive Formulas?**

Answer: Yes, dimensional formulae are used to derive formulas for physical quantities. By analyzing the dimensions on both sides of an equation, relationships between different physical quantities can be established.

Class 11th CBSE Physics Chapters |

Chapter1: UNITS AND MEASUREMENTS |

> Introduction |

>The international system of units |

>Significant figures |

> Dimensions of physical quantities |

> Dimensional analysis and its applications |

Chapter3: MOTION IN A PLANE |

Chapter4: LAWS OF MOTION |

Chapter5: WORK, ENERGY AND POWER |

Chapter6: SYSTEM OF PARTICLES AND ROTATIONAL MOTION |

Chapter7: GRAVITATION |

Chapter8: MECHANICAL PROPERTIES OF SOLIDS |

Chapter9: MECHANICAL PROPERTIES OF FLUIDS |

Chapter10: THERMAL PROPERTIES OF MATTER |

Chapter12: KINETIC THEORY |

Chapter13: OSCILLATIONS |

Chapter14: WAVES |

Class 11th CBSE Chemistry Chapters |

Chapter1: SOME BASIC CONCEPTS OF CHEMISTRY |

Chapter2: STRUCTURE OF ATOMS |

Chapter3: CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES |

Chapter4: CHEMICAL BONDING AND MOLECULAR STRUCTURE |

Chapter5: THERMODYNAMICS |

Chapter6: EQUILIBRIUM |

Chapter7: REDOX REACTIONS |

Chapter8: ORGANIC CHEMISTRY - SOME BASIC PRINCIPLE AND TECHNIQUES |

Chapter9: Hydrocarbons HYDROCARBONS |

Class 11th CBSE Mathematics chapters |

Chapter1: SETS |

Chapter2: RELATIONS AND FUNCTIONS |

Chapter3: TRIGONOMETRIC FUNCTIONS |

Chapter4: COMPLEX NUMBER AND QUADRATIC EQUATIONS |

Chapter5: LINEAR INEQUALITIES |

Chapter6: PERMUTATIONS AND COMBINATIONS |

Chapter7: BINOMIAL THEOREM |

Chapter8: SEQUENCES AND SERIES |

Chapter9: STRAIGHT LINES |

Chapter10: CONIC SECTIONS |

Chapter11: INTRODUCTION TO THREE-DIMENSIONAL GEOMETRY |

Chapter12: LIMITS AND DERIVATIVES |

Chapter13: STATISTICS |

Chapter14: PROBABILITY |

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