Dimensional formula $ML^2T^{-3}$ represents

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Accepted Answer

1. **Definition:** Power ($P$) is defined as the rate of doing work, given by the formula $P = \frac{	ext{Work}}{	ext{Time}}$.
2. **Dimensional Analysis:** 
   - The dimensional formula for Work ($W$) is $[ML^2T^{-2}]$ (derived from Force $	imes$ Displacement: $[MLT^{-2}] \cdot [L]$).
   - The dimensional formula for Time ($t$) is $[T]$.
   - Substituting these into the power formula: 
     $$ [P] = \frac{[ML^2T^{-2}]}{[T]} = [ML^2T^{-3}] $$
3. **Comparison with Options:**
   - **Force:** $[MLT^{-2}]$
   - **Power:** $[ML^2T^{-3}]$
   - **Energy:** $[ML^2T^{-2}]$ (Same as Work)
   - **Work:** $[ML^2T^{-2}]$
4. **Conclusion:** The dimensional formula $[ML^2T^{-3}]$ corresponds to Power. This is explicitly listed in the NCERT Physics Appendices.

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