Dimensional Analysis
Units & Measurements
66
JEE Qs
3%
Hard
60
min
Master the Principle of Homogeneity to quickly verify the correctness of any physical equation and to derive simple relations between physical quantities.
🧮 Key Formulas
✅ Key Points for JEE
- 1The Principle of Homogeneity states that the dimensions of all terms on both sides of a physical equation must be identical; this is the primary tool for checking equation correctness.
- 2Dimensional analysis can be used to derive relations between physical quantities by assuming a simple power law dependence (e.g., F ∝ m^a v^b r^c) and comparing dimensions.
- 3It is effectively used to convert the numerical value of a physical quantity from one system of units (e.g., SI) to another (e.g., CGS) by ensuring dimensional consistency.
- 4Arguments of trigonometric, exponential, and logarithmic functions must be dimensionless, and the terms added or subtracted in an equation must individually possess the same dimensions.
- 5Limitations include inability to determine dimensionless constants, failure to derive relations involving more than three fundamental quantities (in mechanics), and direct inability to handle equations with trigonometric/exponential/logarithmic functions.
⚠️ Common Mistakes
- ✕Forgetting that arguments of trigonometric, exponential, or logarithmic functions must always be dimensionless.
- ✕Incorrectly applying the principle of homogeneity, such as comparing the overall dimensions of LHS and RHS instead of ensuring *each term* in a sum/difference has the same dimension.
- ✕Errors in manipulating exponents during dimensional calculations (e.g., miscalculating L^2 * L^-1 or powers within square roots).
- ✕Attempting to use dimensional analysis to determine the value of dimensionless constants or to derive relations that are not simple power laws.
📝 Practice Questions
See allQ43.The maximum percentage error in the measurment of density of a wire is [Given, mass of wire = (0.60 ± 0.003)g radius of wire = (0.50 ± 0.01)cm length of wire = (10.00 ± 0.05)cm] (1) 8 (2) 5 (3) 4 (4) 7 for another diatomic molecules, but for rigid molecules and γ2 =
Q43.The energy of a system is given as E(t) = α3e−βt , where t is the time and β = 0.3 s−1 . The errors in the measurement of α and t are 1.2% and 1.6% , respectively. At t = 5 s, maximum percentage error in the energy is : (1) 6% (2) 8.4% (3) 11.6% (4) 4%
Q39.Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below. (1) Statement I is true but Statement II is false (2) Statement I is false but Statement II is true (3) Both Statement I and Statement II are false (4) Both Statement I and Statement II are true 2025 (22 Jan Shift 1) JEE Main Previous Year Paper
Q40.Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge, (1) [F] = [C2M−1 L−2 T2] (2) [F] = [C2M−2 L2 T2] (3) [F] = [CM−2 L−2 T−2] (4) [F] = [CM−1 L−2 T2]
Q28.The position of a particle moving on x-axis is given by x(t) = A sin t + B cos2 t + Ct2 + D , where t is time. The dimension of ABC is D (1) L2T −2 (2) L2 (3) L (4) L3 T−2
Q45.For an experimental expression y = 32.3×112527.4 , where all the digits are significant. Then to report the value of y we should write (1) y = 1326.19 (2) y = 1330 (3) y = 1326.186 (4) y = 1326.2
NCERT Chapters
- Class 11 Physics Ch 2: Units and Measurements