Error Analysis — Propagation of errors (add, multiply, power)
Units & Measurements
10
JEE Qs
8%
Hard
75
min
Always remember that errors combine in a way that maximizes uncertainty, so errors are always added, never subtracted, to find the maximum possible error in a combined quantity.
🧮 Key Formulas
✅ Key Points for JEE
- 1In all mathematical operations (addition, subtraction, multiplication, division, power), errors always add up to give the maximum possible error in the final result.
- 2For addition and subtraction (Z = A ± B), the absolute errors are added: `delta_Z = delta_A + delta_B`.
- 3For multiplication and division (Z = A * B or Z = A / B), the fractional (or percentage) errors are added: `delta_Z / Z = (delta_A / A) + (delta_B / B)`.
- 4When a quantity is raised to a power 'n' (e.g., Z = A^n), its fractional error is multiplied by the absolute value of 'n': `delta_Z / Z = |n| * (delta_A / A)`.
- 5The final reported value must include both the calculated result and its propagated error, rounded off to an appropriate number of significant figures or decimal places consistent with the error's precision.
⚠️ Common Mistakes
- ✕Subtracting errors for difference or division operations instead of always adding them to find the maximum possible uncertainty.
- ✕Confusing absolute error (ΔA) with fractional error (ΔA/A) and applying the wrong type of error propagation rule for a given operation.
- ✕Incorrectly applying the power rule, either by forgetting to take the absolute value of the power or by multiplying it with the absolute error instead of the fractional error.
- ✕Failing to round off the final answer and the propagated error correctly, often violating significant figure or decimal place rules.
📝 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