Dimensional Analysis — Checking correctness of equations
Units & Measurements
10
JEE Qs
8%
Hard
40
min
Thoroughly practice deriving dimensional formulas for a wide range of physical quantities, as this is the foundational skill required for all dimensional analysis problems.
🧮 Key Formulas
✅ Key Points for JEE
- 1The Principle of Homogeneity of Dimensions states that an equation is dimensionally correct if the dimensions of all terms on both sides of the equation are the same.
- 2Only physical quantities having the same dimensions can be added or subtracted.
- 3Dimensional analysis checks for dimensional consistency, not for the absolute correctness of a physical equation; it cannot confirm dimensionless constants or numerical factors.
- 4Arguments of trigonometric, logarithmic, and exponential functions must always be dimensionless.
⚠️ Common Mistakes
- ✕Assuming dimensional correctness implies physical correctness (ignoring dimensionless constants like 1/2 in 1/2 mv^2).
- ✕Incorrectly identifying the dimensions of derived physical quantities (e.g., energy, pressure, power).
- ✕Failing to apply the principle of homogeneity to each individual term when quantities are added or subtracted (e.g., assuming [A+B] doesn't require [A] = [B]).
📝 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