Several physically different quantities share the same dimensional formula. This is a frequent JEE trap.
| Dimensions | Quantities |
|---|---|
| [ML^2T^{-2}] | Work, Energy, Torque, Heat |
| [ML^{-1}T^{-2}] | Pressure, Stress, Young's modulus, Bulk modulus, Energy density |
| [MLT^{-1}] | Momentum, Impulse |
| [ML^2T^{-1}] | Angular momentum, Planck's constant |
| [MT^{-2}] | Surface tension, Spring constant, Force gradient |
| [M^0L^0T^0] | Angle, Strain, Relative density, Refractive index |
Key takeaway: Having the same dimensions is necessary but not sufficient for physical equivalence.