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NEET PHYSICSUNITS AND MEASUREMENTSEasy

Question

Which one has the dimensions different from the remaining three?

A

Power

B

Work

C

Torque

D

Energy

Step-by-Step Solution

To determine which quantity has different dimensions, we examine the dimensional formula for each:

  1. Work and Energy: Work (W=F⋅dW = \mathbf{F} \cdot \mathbf{d}) and all forms of energy (kinetic, potential, etc.) have the same dimensions . Since Force has dimensions [MLT−2][MLT^{-2}] and distance is [L][L], Work and Energy have dimensions of [ML2T−2][ML^2T^{-2}] .
  2. Torque: Torque is defined as the moment of force (τ=r×Fτ = \mathbf{r} \times \mathbf{F}) . Its magnitude is force times the perpendicular distance, giving it the same dimensions as work or energy: [ML2T−2][ML^2T^{-2}] .
  3. Power: Power (PP) is defined as the rate of doing work (P=W/tP = W/t) . Dividing the dimensions of work ([ML2T−2][ML^2T^{-2}]) by time ([T][T]) gives the dimensions for power as [ML2T−3][ML^2T^{-3}] .

Comparing the results, Power ([ML2T−3][ML^2T^{-3}]) is the only quantity with dimensions different from the others ([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.

PHYSICSUNITS AND MEASUREMENTSdimensionsdifferentremaining

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