Physical World and Measurement
What this domain tests
Physical World and Measurement tests how confidently you handle SI units, dimensions, significant figures, errors and instruments. BIEAP questions often ask a dimensional check, unit conversion, percentage error, or least-count reasoning rather than memory of definitions.
Core rules
- The seven SI base units are metre, kilogram, second, ampere, kelvin, mole and candela. Derived units are combinations; newton = kg m s^-2, joule = N m, watt = J s^-1.
- Dimensions obey multiplication and division, not addition. Every term in a valid equation must have the same dimensions.
- Absolute error = |measured - accepted|; relative error = absolute/measured; percentage error = relative × 100.
- For Z = A^p B^q / C^r, fractional error = p(ΔA/A) + q(ΔB/B) + r(ΔC/C), with powers taken as positive magnitudes.
- In significant figures, multiplication/division keeps the least number of significant figures; addition/subtraction keeps the least number of decimal places.
Worked example
A force F = kx restores a spring, where x is extension. Find the dimensions of k and its SI unit. From F = kx, k = F/x. Dimensions: [k] = [MLT^-2]/[L] = [MT^-2]. SI unit: kg s^-2, equivalent to N m^-1. The reasoning is a dimensional equation, not a numerical substitution.
Traps
Do not treat dimensionless quantities such as angle, strain or refractive index as having units. Do not drop the absolute value when adding errors. A least-count error belongs to the instrument, not to the object. When converting cm^2 to m^2, square the factor 10^-2.