Complete Study Material for JEE, NEET, CBSE Board Class 11 Exams
Understanding dimensional analysis is crucial in physics, especially for students preparing for exams like JEE, NEET, and CBSE Board Class 11. This concept helps in verifying equations, converting units, and checking the correctness of derived formulas. Below is a comprehensive explanation of quantities having the same dimensions, categorized systematically.
Thermal capacity, gas constant, Boltzmann constant, entropy
12
M⁰L⁰T¹
L/R, √LC, RC (L = Inductance, R = Resistance, C = Capacitance)
13
M¹L²T⁻²
I2Rt, VIt, V2/Rt,qV, LI2, q2/C, CV2, Various electrical quantities involving L=inductance, C=capacitance, q=charge, R=resistance, I=Current and V=voltage
Conceptual Questions & Answers
Q1: Why is dimensional analysis important in physics?
A: Dimensional analysis helps check the correctness of equations, derive new formulas, and convert units between different measurement systems.
Q2: Why do work and torque have the same dimensions but different physical meanings?
A: Though both have dimensions M¹L²T⁻², work is a scalar quantity representing energy transfer, whereas torque is a vector quantity causing rotational motion.
Q3: What are dimensionless quantities? Give examples.
A: Dimensionless quantities have no physical dimensions. Examples include strain, refractive index, relative density, and solid angle.
MCQs with Answers & Explanation
Q1: Which of the following pairs have the same dimensions?
(a) Work and torque (b) Force and pressure (c) Momentum and energy (d) Strain and stress
Answer: (a) Work and torque Explanation: Both have dimensions M¹L²T⁻², but torque is a rotational effect, while work is energy transfer.
Q2: What is the dimensional formula of Planck’s constant?
(a) M⁰L²T⁻² (b) M¹L²T⁻¹ (c) M¹L¹T⁻² (d) M¹L⁰T⁻²
Answer: (b) M¹L²T⁻¹ Explanation: Planck’s constant has dimensions of angular momentum, which matches M¹L²T⁻¹.
Do You Know?
Energy and torque have the same dimensions but represent different physical concepts.
Pressure and stress share dimensions because they both quantify force per unit area.
Dimensional analysis is used in checking the validity of scientific equations.
Worksheet
Find the dimensional formula of energy density.
Show that surface tension and surface energy have the same dimensions.
Verify whether the equation v=u+atv = u + at is dimensionally correct.
Convert 1 Joule into ergs using dimensional analysis.
Test Paper (Marks Distribution)
Section A: Conceptual Questions (10 Marks)
Define dimensional analysis. (2 Marks)
Why is strain a dimensionless quantity? (2 Marks)
Explain the significance of Planck’s constant. (2 Marks)
Differentiate between pressure and stress. (4 Marks)
Section B: Numerical Questions (10 Marks)
Derive the dimensional formula of impulse. (5 Marks)
Show that work and torque have the same dimensions. (5 Marks)
Section C: MCQs (10 Marks)
What is the dimension of momentum? (2 Marks)
Which quantity has the dimensional formula M¹L¹T⁻²? (2 Marks)
Work and energy share the same dimensions because: (2 Marks)
Why is refractive index dimensionless? (2 Marks)
What is the SI unit of Planck’s constant? (2 Marks)
Test Your Knowledge (Quiz)
Physical Quantities Quiz
Important Points for Quick Revision
Dimensional analysis helps in checking the correctness of equations.
Quantities with the same dimensions can have different physical meanings.
Dimensionless quantities do not have fundamental dimensions.
Conversion of units is simplified using dimensional formulas.
MCQs and conceptual questions are crucial for competitive exams.
