Complete Study Material for JEE, NEET, CBSE Board Class 11 Exams
Physics is a fundamental branch of science that deals with the study of matter, energy, and the interactions between them. Understanding the dimensions of physical quantities is crucial for solving problems in mechanics, which is an essential topic for competitive exams like JEE, NEET, and CBSE Board Class 11. In this article, we will discuss the dimensional analysis of key physical quantities in mechanics, followed by FAQs, MCQs, conceptual questions, worksheets, and a test paper.
List of Important Physical Quantities, Units, and Their Dimensions in Mechanics
| S. No | Quantity | Unit | Dimension |
|---|---|---|---|
| 1 | Velocity or speed (v) | m/s | [M⁰L¹T⁻¹] |
| 2 | Acceleration (a) | m/s² | [M⁰L¹T⁻²] |
| 3 | Momentum (P) | kg-m/s | [M¹L¹T⁻¹] |
| 4 | Impulse (I) | Newton-sec or kg-m/s | [M¹L¹T⁻¹] |
| 5 | Force (F) | Newton | [M¹L¹T⁻²] |
| 6 | Pressure (P) | Pascal | [M¹L⁻¹T⁻²] |
| 7 | Kinetic energy (Eₖ) | Joule | [M¹L²T⁻²] |
| 8 | Power (P) | Watt or Joule/s | [M¹L²T⁻³] |
| 9 | Density (d) | kg/m³ | [M¹L⁻³T⁰] |
| 10 | Angular displacement (θ) | Radian (rad) | [M⁰L⁰T⁰] |
| 11 | Angular velocity (ω) | Radian/sec | [M⁰L⁰T⁻¹] |
| 12 | Angular acceleration (α) | Radian/sec² | [M⁰L⁰T⁻²] |
| 13 | Moment of inertia (I) | kg-m² | [M¹L²T⁰] |
| 14 | Torque (τ) | Newton-meter | [M¹L²T⁻²] |
| 15 | Angular momentum (L) | Joule-sec | [M¹L²T⁻¹] |
| 16 | Force constant or spring constant (k) | Newton/m | [M¹L⁰T⁻²] |
| 17 | Gravitational constant (G) | N-m²/kg² | [M⁻¹L³T⁻²] |
| 18 | Intensity of gravitational field (E₉) | N/kg | [M⁰L¹T⁻²] |
| 19 | Gravitational potential (V₉) | Joule/kg | [M⁰L²T⁻²] |
| 20 | Surface tension (T) | N/m or Joule/m² | [M¹L⁰T⁻²] |
| 21 | Velocity gradient (Vg) | Second⁻¹ | [M⁰L⁰T⁻¹] |
| 22 | Coefficient of viscosity (η) | kg/m-s | [M¹L⁻¹T⁻¹] |
| 23 | Stress | N/m² | [M¹L⁻¹T⁻²] |
| 24 | Strain | No unit | [M⁰L⁰T⁰] |
| 25 | Modulus of elasticity (E) | N/m² | [M¹L⁻¹T⁻²] |
| 26 | Poisson Ratio (σ) | No unit | [M⁰L⁰T⁰] |
| 27 | Time period (T) | Second | [M⁰L⁰T¹] |
| 28 | Frequency (n) | Hz | [M⁰L⁰T⁻¹] |
Question-Answer for CBSE Board Exams
Q1: Why is dimensional analysis important in physics?
Ans: Dimensional analysis helps verify equations, check correctness, and derive new relations between physical quantities.
Q2: What is the dimension of gravitational constant (G)?
Ans: The dimension of gravitational constant (G) is [M⁻¹L³T⁻²].
Do You Know?
- The dimensional formula for work and energy is the same.
- The unit of force is named after Sir Isaac Newton.
- Stress and pressure have the same dimensions but different physical meanings.
Multiple Choice Questions (MCQs)
Q1: The SI unit of power is:
- (A) Joule
- (B) Newton
- (C) Watt
- (D) Pascal
Answer: (C) Watt
Explanation: Power is the rate at which work is done, and its unit is Watt (Joule/sec).
Q2: Which of the following quantities has no dimensions?
- (A) Acceleration
- (B) Angle
- (C) Force
- (D) Pressure
Answer: (B) Angle
Explanation: Angle is a dimensionless quantity as it is the ratio of two lengths.
Worksheet for Practice
- Write the dimensional formula for torque and moment of inertia.
- How is the dimensional formula of force related to Newton’s Second Law?
- Find the dimensions of surface tension.
Test Paper (50 Marks)
Section A: Multiple Choice Questions (5 × 2 = 10 Marks)
- What is the unit of impulse?
- The dimensional formula of work is?
- What is the SI unit of power?
- Which of the following quantities has no dimensions?
- What is the dimensional formula of force?
Section B: Short Answer Questions (4 × 5 = 20 Marks)
- Derive the dimensional formula of modulus of elasticity.
- Why does power have a dimension of [M¹L²T⁻³]?
- Explain the significance of dimensional analysis in physics.
- Find the dimensions of surface tension and stress.
Section C: Long Answer Questions (2 × 10 = 20 Marks)
- Explain how dimensional analysis helps in checking the correctness of equations with examples.
- Derive the relation between force, mass, and acceleration using dimensional analysis.
Test Your Knowledge(Quiz)
Physics Quiz
Important Points for Quick Revision
- Velocity = [M⁰L¹T⁻¹]
- Force = [M¹L¹T⁻²]
- Pressure = [M¹L⁻¹T⁻²]
- Energy = [M¹L²T⁻²]
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