Part of JME-07 — Units, Measurements & Error Analysis

Same Dimensions — Different Quantities

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DimensionsQuantities
[ML^{2T}^{-2}]Work, Energy, Torque, Heat
[ML^{-1}$$T^{-2}]Pressure, Stress, Young's modulus, Bulk modulus, Energy density
[MLT1MLT^{-1}]Momentum, Impulse
[ML^{2T}^{-1}]Angular momentum, Planck's constant
[MT2MT^{-2}]Surface tension, Spring constant, Force gradient
[M^{0L}^{0T}^0]Angle, Strain, Relative density, Refractive index, Mach number

This table is frequently tested in JEE. Remember: same dimensions is necessary but not sufficient for physical equivalence. Work (scalar) and torque (vector) are fundamentally different despite identical dimensions.

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