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NEET PHYSICSUNITS AND MEASUREMENTSEasy

Question

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=F⋅dW = \mathbf{F} \cdot \mathbf{d}). Its dimensional formula is [ML2T−2][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 [ML2T−2][ML^2T^{-2}] .
  3. Power (PP): Defined as the rate of doing work (P=W/tP = W/t). Its dimensions are [ML2T−3][ML^2T^{-3}] .
  4. Momentum (pp): Defined as the product of mass and velocity (p=mvp = mv). Its dimensions are [MLT−1][MLT^{-1}] .
  5. Force (FF): Defined as mass times acceleration (F=maF = ma). Its dimensions are [MLT−2][MLT^{-2}] .

Conclusion: Comparing the dimensions, Work and Energy both possess the dimensional formula [ML2T−2][ML^2T^{-2}].

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from UNITS AND MEASUREMENTS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

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