Nature of Physical World and Measurement
What this domain tests
The Nature of Physical World and Measurement unit checks whether you can choose SI units, write dimensional formulae, propagate errors and read vernier and screw-gauge scales. Tamil Nadu HSE questions often combine a definition with a numerical least-count or percentage-error part.
Core rules
- SI base units: metre, kilogram, second, ampere, kelvin, mole, candela.
- Dimensional formula: velocity LT⁻¹, force MLT⁻², energy ML²T⁻², pressure ML⁻¹T⁻².
- Dimensional analysis checks equations and converts units, but cannot find dimensionless constants or test equations containing trig or exponential terms.
- For a quantity q = xᵃyᵇ/zᶜ, relative error Δq/q = |a|Δx/x + |b|Δy/y + |c|Δz/z.
- Least count of vernier = 1 MSD − 1 VSD; of screw gauge = pitch/number of circular divisions.
Worked example
A cylinder has m = (2.00 ± 0.01) g, r = (0.50 ± 0.01) cm and l = (4.00 ± 0.01) cm. Density ρ = m/(πr²l). Relative error = Δm/m + 2Δr/r + Δl/l = 0.005 + 0.04 + 0.0025 = 0.0475, so percentage error = 4.75%. The radius term doubles because r is squared; π is treated as exact for this purpose.
Traps
Adding absolute errors instead of relative errors; forgetting the power 2 on radius; applying a screw-gauge zero error with the wrong sign; quoting more significant figures than the data allow; treating a dimensionless constant as dimensionally determined.