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NEET PHYSICSUNITS AND MEASUREMENTSEasy

Question

Dimensional formula for volume elasticity is

A

M¹L⁻²T⁻²

B

M¹L⁻³T⁻²

C

M¹L²T⁻²

D

M¹L⁻¹T⁻²

Step-by-Step Solution

Volume elasticity, often referred to as the Bulk Modulus (BB or KK), is defined as the ratio of hydraulic stress to the corresponding volumetric strain.

  1. Formula: K=StressVolumetric Strain=−PΔV/VK = \frac{\text{Stress}}{\text{Volumetric Strain}} = \frac{-P}{\Delta V / V}.
  2. Dimensional Analysis:
  • Stress (Pressure): Force per unit area. Dimensions = [MLT−2][L2]=[ML−1T−2]\frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}] .
  • Volumetric Strain: Ratio of change in volume to original volume (ΔV/V\Delta V/V). Since it is a ratio of identical quantities, it is dimensionless [M0L0T0][M^0L^0T^0] .
  1. Result: The dimensions of volume elasticity are the same as stress or pressure. [K]=[ML−1T−2]=[M1L−1T−2][K] = \frac{[ML^{-1}T^{-2}]}{} = [M^1L^{-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.

PHYSICSUNITS AND MEASUREMENTSdimensionalformulavolumeelasticity

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