Dimensional Formula

Question

Which of the following physical quantities does NOT have the dimensional formula [M⁰L⁰T⁻¹]?

RankGuru · Accepted Answer

1. **Frequency ($f$)**: Defined as number of cycles per unit time. $[f] = [T^{-1}]$.
2. **Velocity Gradient**: Rate of change of velocity with distance ($dv/dx$).
   - Dimensions: $\frac{[LT^{-1}]}{[L]} = [T^{-1}]$.
3. **Angular Velocity ($\omega$)**: Angle (dimensionless) swept per unit time.
   - Dimensions: $\frac{1}{[T]} = [T^{-1}]$.
4. **Angular Acceleration ($\alpha$)**: Rate of change of angular velocity ($d\omega/dt$).
   - Dimensions: $\frac{[T^{-1}]}{[T]} = [T^{-2}]$.
5. **Conclusion**: Only **Angular Acceleration** has different dimensions ($[M^0 L^0 T^{-2}]$).

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