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NEET PHYSICSEasy

Which of the following pairs of physical quantities has the same dimensions?

A

Work and power

B

Momentum and energy

C

Force and power

D

Work and energy

Step-by-Step Solution

To determine which pair has the same dimensions, we analyze the dimensional formulae of the given quantities:

  1. Work (WW): Defined as the product of force and displacement (W=FdW = \mathbf{F} \cdot \mathbf{d}). Its dimensional formula is [ML2T2][ML^2T^{-2}] .
  2. Energy (EE): Energy is the capacity to do work. Kinetic energy (K=12mv2K = \frac{1}{2}mv^2) and potential energy have the same dimensions as work, which is [ML2T2][ML^2T^{-2}] .
  3. Power (PP): Defined as the rate of doing work (P=W/tP = W/t). Its dimensions are [ML2T3][ML^2T^{-3}] .
  4. Momentum (pp): Defined as the product of mass and velocity (p=mvp = mv). Its dimensions are [MLT1][MLT^{-1}] .
  5. Force (FF): Defined as mass times acceleration (F=maF = ma). Its dimensions are [MLT2][MLT^{-2}] .

Conclusion: Comparing the dimensions, Work and Energy both possess the dimensional formula [ML2T2][ML^2T^{-2}].

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