JEE Main 2026 – Units and Measurements Important PYQs
Q1. A physical quantity C is related to p, q, r, s as C = pq² / (r³√s). Percentage errors in p, q, r, s are 1%, 2%, 3%, and 2%. Find the percentage error in C.
Q2. For determination of refractive index of glass slab, a travelling microscope is used whose main scale has 300 divisions equal to 15 cm and vernier has 25 divisions = 24 main divisions. Find least count (LC).
Q3. A rectangular metal sheet has dimensions 5 mm × 2.5 mm. Using screw gauge (pitch 0.75 mm, 15 divisions), find maximum fractional error in area measurement.
Q4. Match List I (Physical Quantity) with List II (Dimensional Formula): (A) Density, (B) Impulse, (C) Power, (D) Moment of Inertia.
Q5. For y = (32.3 × 1125) / 27.4, where all digits are significant, find correct number of significant figures to report y.
Q6. In a vernier calliper, 50 vernier divisions equal 49 main scale divisions. Zero error = 0.04 mm. Find number of main scale divisions in 1 cm.
Q7. A vernier calliper has 20 vernier divisions = 19 main scale divisions. If least count = 0.1 mm, one main scale division equals how many mm?
Q8. A screw gauge with pitch 1 mm has 100 circular divisions. Zero of circular scale lies 5 divisions below reference line. When 4 linear scale divisions visible and 60 circular divisions coincide, find wire diameter.
Q9. A quantity Q = a⁴b³ / c² where percentage errors in a, b, c are 3%, 4%, 5%. Find percentage error in Q.
Q10. For x(t) = A sin t + B cos²t + C t² + D, find the dimension of (A B C)/D.
Quick Notes & Concept Summary
- Least Count: LC = (Value of 1 MSD - Value of 1 VSD). Common in vernier and screw gauge.
- Errors: For multiplication/division, add percentage errors; for power, multiply error with power.
- Significant Figures: Final result should have least number of significant digits among measured quantities.
- Dimensional Analysis: Verify homogeneity of equations and derive formulae using dimensions.
- Units: SI base units include m, kg, s, A, K, mol, cd. Derived units come from these.
These concepts are repeated every year in JEE Main Physics. Solving these 10 questions improves accuracy in error analysis, significant figures and dimensional consistency.