Error Analysis — Types of errors (systematic, random)
Units & Measurements
10
JEE Qs
8%
Hard
40
min
Thoroughly understand the distinct characteristics, common sources, and minimization methods for both systematic and random errors, as conceptual questions are frequent.
✅ Key Points for JEE
- 1Systematic errors have a definite cause and direction, leading to a consistent deviation (either always high or always low) from the true value. They affect the accuracy of the measurement.
- 2Sources of systematic errors include instrumental errors (e.g., faulty calibration, zero error), imperfections in experimental technique, and personal errors (e.g., parallax error).
- 3Systematic errors can be minimized or eliminated by identifying their source, applying corrections, or improving the experimental technique/instrumentation.
- 4Random errors are unpredictable fluctuations that occur due to unknown and variable causes. They can cause deviations in either direction (positive or negative) and primarily affect the precision of the measurement.
- 5Random errors cannot be eliminated but can be reduced by taking a large number of readings and calculating their arithmetic mean. This helps positive and negative deviations to statistically cancel out.
⚠️ Common Mistakes
- ✕Confusing systematic and random errors, especially regarding their causes and methods of reduction. Forgetting that systematic errors can be eliminated, while random errors can only be reduced.
- ✕Incorrectly classifying errors in given experimental scenarios (e.g., mistaking a zero error for a random error).
- ✕Failing to understand the relationship between systematic errors and accuracy, and random errors and precision.
📝 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