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NEET PHYSICSUNITS AND MEASUREMENTSEasy

Question

The dimensions of shear modulus are

A

MLT−1MLT^{-1}

B

ML2T−2ML^2T^{-2}

C

ML−1T−2ML^{-1}T^{-2}

D

MLT−2MLT^{-2}

Step-by-Step Solution

  1. Definition: Shear modulus (modulus of rigidity) is defined as the ratio of shear stress to shear strain.
  2. Dimensional Analysis:
  • Shear strain is the ratio of relative displacement to length (Δx/L\Delta x / L), making it a dimensionless quantity [M0L0T0][M^0L^0T^0].
  • Shear stress is defined as force per unit area (F/AF/A). The dimensions of force are [MLT−2][MLT^{-2}] and the dimensions of area are [L2][L^2].
  • Therefore, the dimensions of shear stress are [MLT−2][L2]=[ML−1T−2]\frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}].
  1. Conclusion: Since shear strain is dimensionless, the dimensions of shear modulus are exactly the same as those of shear stress, which is [ML−1T−2][ML^{-1}T^{-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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