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NEET PHYSICSUNITS AND MEASUREMENTSMedium

Question

Which of the following pair does not have similar dimensions?

A

Stress and pressure

B

Angle and strain

C

Tension and surface tension

D

Planck's constant and angular momentum

Step-by-Step Solution

  1. Stress and Pressure: Both stress and pressure are defined as force per unit area. Therefore, they have the same dimensional formula: [ML−1T−2][ML^{-1}T^{-2}] .
  2. Angle and Strain: Angle is the ratio of arc to radius, and strain is the ratio of change in dimension to original dimension. Both are ratios of identical physical quantities and are dimensionless: [M0L0T0][M^0L^0T^0] .
  3. Tension and Surface Tension: Tension is a type of force, so its dimensional formula is [MLT−2][MLT^{-2}] . Surface tension is defined as force per unit length, so its dimensional formula is [MLT−2][L]=[ML0T−2]\frac{[MLT^{-2}]}{[L]} = [ML^0T^{-2}] or [MT−2][MT^{-2}] . These are not similar.
  4. Planck's constant and Angular momentum: From E=hνE = h\nu, the dimensions of Planck's constant hh are [ML2T−2][T−1]=[ML2T−1]\frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}]. Angular momentum L=mvrL = mvr has dimensions [M][LT−1][L]=[ML2T−1][M][LT^{-1}][L] = [ML^2T^{-1}]. Both have the same dimensions .

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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